Fundamentals Of Infinite Dimensional Representation Theory

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Fundamentals of Infinite Dimensional Representation Theory

Raymond C. Fabec
Fundamentals of Infinite Dimensional Representation Theory Book PDF

Author : Raymond C. Fabec
Publisher : CRC Press
Page : 448 pages
File Size : 48,7 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781482285772

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Fundamentals of Infinite Dimensional Representation Theory by Raymond C. Fabec Pdf

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Infinite-dimensional Representations of 2-groups

Anonim
Infinite dimensional Representations of 2 groups Book PDF

Author : Anonim
Publisher : Unknown
Page : 120 pages
File Size : 43,9 Mb
Release : 2012
Category : Categories
ISBN : 0821891162

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Infinite-dimensional Representations of 2-groups by Anonim Pdf

A `2-group' is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, 2-groups have representations on `2-vector spaces', which are categories analogous to vector spaces. Unfortunately, Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. For this reason, Crane, Sheppeard and Yetter introduced certain infinite-dimensional 2-vector spaces called `measurable categories' (since they are closely related to measurable fields of Hilbert spaces), and used these to study infinite-dimensional representations of certain Lie 2-groups. Here we continue this work. We begin with a detailed study of measurable categories. Then we give a geometrical description of the measurable representations, intertwiners and 2-intertwiners for any skeletal measurable 2-group. We study tensor products and direct sums for representations, and various concepts of subrepresentation. We describe direct sums of intertwiners, and sub-intertwiners--features not seen in ordinary group representation theory. We study irreducible and indecomposable representations and intertwiners. We also study `irretractable' representations--another feature not seen in ordinary group representation theory. Finally, we argue that measurable categories equipped with some extra structure deserve to be considered `separable 2-Hilbert spaces', and compare this idea to a tentative definition of 2-Hilbert spaces as representation categories of commutative von Neumann algebras.

Infinite-dimensional Aspects of Representation Theory and Applications

Stephen Berman
Infinite dimensional Aspects of Representation Theory and Applications Book PDF

Author : Stephen Berman
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 52,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837016

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Infinite-dimensional Aspects of Representation Theory and Applications by Stephen Berman Pdf

The University of Virginia (Charlottesville) hosted an international conference on Infinite-dimensional Aspects of Representation Theory and Applications. This volume contains papers resulting from the mini-courses and talks given at the meeting. Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. The specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. The book is suitable for graduate students and researchers interested in representation theory.

A Journey Through Representation Theory

Caroline Gruson,Vera Serganova
A Journey Through Representation Theory Book PDF

Author : Caroline Gruson,Vera Serganova
Publisher : Springer
Page : 223 pages
File Size : 47,7 Mb
Release : 2018-10-23
Category : Mathematics
ISBN : 9783319982717

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A Journey Through Representation Theory by Caroline Gruson,Vera Serganova Pdf

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

Infinite Dimensional Lie Groups in Geometry and Representation Theory

Augustin Banyaga,Joshua A Leslie,Thierry Robart
Infinite Dimensional Lie Groups in Geometry and Representation Theory Book PDF

Author : Augustin Banyaga,Joshua A Leslie,Thierry Robart
Publisher : World Scientific
Page : 176 pages
File Size : 52,5 Mb
Release : 2002-07-12
Category : Science
ISBN : 9789814488143

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Infinite Dimensional Lie Groups in Geometry and Representation Theory by Augustin Banyaga,Joshua A Leslie,Thierry Robart Pdf

This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:

Infinite Dimensional Groups and Algebras in Quantum Physics

Johnny T. Ottesen
Infinite Dimensional Groups and Algebras in Quantum Physics Book PDF

Author : Johnny T. Ottesen
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 54,7 Mb
Release : 2008-09-11
Category : Science
ISBN : 9783540491415

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Infinite Dimensional Groups and Algebras in Quantum Physics by Johnny T. Ottesen Pdf

The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.

Introduction to Representation Theory

Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Introduction to Representation Theory Book PDF

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 54,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

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Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

Palle Jorgensen,James Tian
Infinite dimensional Analysis Operators In Hilbert Space Stochastic Calculus Via Representations And Duality Theory Book PDF

Author : Palle Jorgensen,James Tian
Publisher : World Scientific
Page : 253 pages
File Size : 47,8 Mb
Release : 2021-01-15
Category : Mathematics
ISBN : 9789811225796

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Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf

The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Group Representations, Ergodic Theory, and Mathematical Physics

Robert S. Doran,Calvin C. Moore,Robert J. Zimmer
Group Representations Ergodic Theory and Mathematical Physics Book PDF

Author : Robert S. Doran,Calvin C. Moore,Robert J. Zimmer
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 49,5 Mb
Release : 2008
Category : Ergodic theory
ISBN : 9780821842256

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Group Representations, Ergodic Theory, and Mathematical Physics by Robert S. Doran,Calvin C. Moore,Robert J. Zimmer Pdf

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.

Developments and Trends in Infinite-Dimensional Lie Theory

Karl-Hermann Neeb,Arturo Pianzola
Developments and Trends in Infinite Dimensional Lie Theory Book PDF

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 52,5 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Representation Theory of Lie Groups

Jeffrey Adams, David Vogan
Representation Theory of Lie Groups Book PDF

Author : Jeffrey Adams, David Vogan
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 53,8 Mb
Release : 2000-01-25
Category : Mathematics
ISBN : 0821886908

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Representation Theory of Lie Groups by Jeffrey Adams, David Vogan Pdf

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant ``philosophy of coadjoint orbits'' for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of ``localization''. And Jian-Shu Li covers Howe's theory of ``dual reductive pairs''. Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory.

Transfer Operators, Endomorphisms, and Measurable Partitions

Sergey Bezuglyi,Palle E. T. Jorgensen
Transfer Operators Endomorphisms and Measurable Partitions Book PDF

Author : Sergey Bezuglyi,Palle E. T. Jorgensen
Publisher : Springer
Page : 162 pages
File Size : 42,8 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9783319924175

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Transfer Operators, Endomorphisms, and Measurable Partitions by Sergey Bezuglyi,Palle E. T. Jorgensen Pdf

The subject of this book stands at the crossroads of ergodic theory and measurable dynamics. With an emphasis on irreversible systems, the text presents a framework of multi-resolutions tailored for the study of endomorphisms, beginning with a systematic look at the latter. This entails a whole new set of tools, often quite different from those used for the “easier” and well-documented case of automorphisms. Among them is the construction of a family of positive operators (transfer operators), arising naturally as a dual picture to that of endomorphisms. The setting (close to one initiated by S. Karlin in the context of stochastic processes) is motivated by a number of recent applications, including wavelets, multi-resolution analyses, dissipative dynamical systems, and quantum theory. The automorphism-endomorphism relationship has parallels in operator theory, where the distinction is between unitary operators in Hilbert space and more general classes of operators such as contractions. There is also a non-commutative version: While the study of automorphisms of von Neumann algebras dates back to von Neumann, the systematic study of their endomorphisms is more recent; together with the results in the main text, the book includes a review of recent related research papers, some by the co-authors and their collaborators.

Geometric Fundamentals of Robotics

J.M. Selig
Geometric Fundamentals of Robotics Book PDF

Author : J.M. Selig
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 51,8 Mb
Release : 2007-12-13
Category : Technology & Engineering
ISBN : 9780387272740

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Geometric Fundamentals of Robotics by J.M. Selig Pdf

* Provides an elegant introduction to the geometric concepts that are important to applications in robotics * Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry * An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics

Reflection Positivity

Karl-Hermann Neeb,Gestur Ólafsson
Reflection Positivity Book PDF

Author : Karl-Hermann Neeb,Gestur Ólafsson
Publisher : Springer
Page : 139 pages
File Size : 47,8 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9783319947556

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Reflection Positivity by Karl-Hermann Neeb,Gestur Ólafsson Pdf

Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the representation theoretic aspects of Refection Positivity and discusses its connections to those different fields on a level suitable for doctoral students and researchers in related fields. It starts with a general introduction to the ideas and methods involving refection positive Hilbert spaces and the Osterwalder--Schrader transform. It then turns to Reflection Positivity in Lie group representations. Already the case of one-dimensional groups is extremely rich. For the real line it connects naturally with Lax--Phillips scattering theory and for the circle group it provides a new perspective on the Kubo--Martin--Schwinger (KMS) condition for states of operator algebras. For Lie groups Reflection Positivity connects unitary representations of a symmetric Lie group with unitary representations of its Cartan dual Lie group. A typical example is the duality between the Euclidean group E(n) and the Poincare group P(n) of special relativity. It discusses in particular the curved context of the duality between spheres and hyperbolic spaces. Further it presents some new integration techniques for representations of Lie algebras by unbounded operators which are needed for the passage to the dual group. Positive definite functions, kernels and distributions and used throughout as a central tool.

Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups

Ludwig Pittner
Algebraic Foundations of Non Commutative Differential Geometry and Quantum Groups Book PDF

Author : Ludwig Pittner
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 45,7 Mb
Release : 2009-01-29
Category : Science
ISBN : 9783540478010

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Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups by Ludwig Pittner Pdf

Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.