A Journey Through Representation Theory

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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 : 50,6 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.

A Tour of Representation Theory

Martin Lorenz
A Tour of Representation Theory Book PDF

Author : Martin Lorenz
Publisher : Unknown
Page : 654 pages
File Size : 42,8 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 1470449056

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A Tour of Representation Theory by Martin Lorenz Pdf

Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is.

Operator Theory, Functional Analysis and Applications

M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Operator Theory Functional Analysis and Applications Book PDF

Author : M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich
Publisher : Springer Nature
Page : 654 pages
File Size : 49,6 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030519452

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Operator Theory, Functional Analysis and Applications by M. Amélia Bastos,Luís Castro,Alexei Yu. Karlovich Pdf

This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.

A Journey through the History of Numerical Linear Algebra

Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia
A Journey through the History of Numerical Linear Algebra Book PDF

Author : Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia
Publisher : SIAM
Page : 813 pages
File Size : 48,6 Mb
Release : 2022-12-06
Category : Mathematics
ISBN : 9781611977233

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A Journey through the History of Numerical Linear Algebra by Claude Brezinski ,Gérard Meurant ,Michela Redivo-Zaglia Pdf

This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

Group Matrices, Group Determinants and Representation Theory

Kenneth W. Johnson
Group Matrices Group Determinants and Representation Theory Book PDF

Author : Kenneth W. Johnson
Publisher : Springer Nature
Page : 384 pages
File Size : 43,5 Mb
Release : 2019-11-08
Category : Mathematics
ISBN : 9783030283001

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Group Matrices, Group Determinants and Representation Theory by Kenneth W. Johnson Pdf

This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.

The Mathematics of Frobenius in Context

Thomas Hawkins
The Mathematics of Frobenius in Context Book PDF

Author : Thomas Hawkins
Publisher : Springer Science & Business Media
Page : 699 pages
File Size : 43,8 Mb
Release : 2013-07-23
Category : Mathematics
ISBN : 9781461463337

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The Mathematics of Frobenius in Context by Thomas Hawkins Pdf

Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices.

Supersymmetric Mechanics - Vol. 1

Stefano Bellucci
Supersymmetric Mechanics Vol 1 Book PDF

Author : Stefano Bellucci
Publisher : Springer
Page : 230 pages
File Size : 45,9 Mb
Release : 2006-08-31
Category : Science
ISBN : 9783540333142

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Supersymmetric Mechanics - Vol. 1 by Stefano Bellucci Pdf

This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. The selected topics include supersymmetry and supergravity, the attractor mechanism, black holes, fluxes, noncommutative mechanics, super-Hamiltonian formalism and matrix models. Incorporates in extensive write-ups the results of animated discussion sessions which followed the individual lectures.

A Tour of Representation Theory

Martin Lorenz
A Tour of Representation Theory Book PDF

Author : Martin Lorenz
Publisher : American Mathematical Soc.
Page : 654 pages
File Size : 55,7 Mb
Release : 2018
Category : Categories (Mathematics)
ISBN : 9781470436803

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A Tour of Representation Theory by Martin Lorenz Pdf

Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.

Semantics, Pragmatics, Philosophy

Kasia M. Jaszczolt
Semantics Pragmatics Philosophy Book PDF

Author : Kasia M. Jaszczolt
Publisher : Cambridge University Press
Page : 439 pages
File Size : 49,8 Mb
Release : 2023-03-31
Category : Language Arts & Disciplines
ISBN : 9781108499651

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Semantics, Pragmatics, Philosophy by Kasia M. Jaszczolt Pdf

Combining semantics, pragmatics, and philosophy, this is a guide on how to think about meaning like a linguist and philosopher.

Representation Theory and Beyond

Jan Šťovíček,Jan Trlifaj
Representation Theory and Beyond Book PDF

Author : Jan Šťovíček,Jan Trlifaj
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 46,9 Mb
Release : 2020-11-13
Category : Education
ISBN : 9781470451318

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Representation Theory and Beyond by Jan Šťovíček,Jan Trlifaj Pdf

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Eva Figes' Writings

Silvia Pellicer-Ortin
Eva Figes Writings Book PDF

Author : Silvia Pellicer-Ortin
Publisher : Cambridge Scholars Publishing
Page : 290 pages
File Size : 54,9 Mb
Release : 2015-10-13
Category : Literary Criticism
ISBN : 9781443884808

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Eva Figes' Writings by Silvia Pellicer-Ortin Pdf

This book provides a general overview of the life and literary career of the prolific writer Eva Figes, placing her extensive production within the various literary movements that have shaped the last century, and drawing on the main features of her works and the different stages in her production. Having recourse to the tools provided by narratology and using the theoretical background of the disciplines of ethics, Holocaust and trauma studies, together with other related fields such as theories of artistic representation, identity questions concerning Jewishness, contemporary history and philosophy, it carries out a comprehensive analysis of Figes’s main works. The main starting hypothesis explored throughout the book is that an evolution may be traced in the aesthetics employed by Figes throughout her career – from her initial Modernist phase to her more realist position – to depict individual and collective traumas. This development is a result of her need to find a mode of representing various traumatic events that have given shape to her personal and family history and to our recent collective history, from the two World Wars and the Holocaust to the social exclusion suffered by minority groups like women or the Jewish immigrant communities. This evolution will be also approached thematically, as there is a development from her early interest in depicting isolated male traumatised characters to the traumas suffered by women under patriarchal structures, and, then, to the encounter with her own suffering as a Holocaust survivor. The author’s evolution in the topics and narrative techniques employed mirrors the different stages in the individual and collective processes of recovery from traumatic experiences, from the process of acting out to the eventual healing phase. Thus, the conclusions detailed here will be useful not only to make Figes’ work known to a wider audience, but also to gain an insight into the evolution of the literary tendencies of the last few decades in trying to represent some of the most horrible events of the modern age.

A Journey through the Universe

Ian Morison
A Journey through the Universe Book PDF

Author : Ian Morison
Publisher : Cambridge University Press
Page : 369 pages
File Size : 46,6 Mb
Release : 2015
Category : Science
ISBN : 9781107073463

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A Journey through the Universe by Ian Morison Pdf

A comprehensive, up-to-date survey of our knowledge of the Universe beyond Earth, for general readers and astronomy enthusiasts.

Operational Spacetime

Heinrich Saller
Operational Spacetime Book PDF

Author : Heinrich Saller
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 55,7 Mb
Release : 2009-10-28
Category : Science
ISBN : 9781441908988

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Operational Spacetime by Heinrich Saller Pdf

The book provides readers with an understanding of the mutual conditioning of spacetime and interactions and matter. The spacetime manifold will be looked at to be a reservoir for the parametrization of operation Lie groups or subgroup classes of Lie groups. With basic operation groups or Lie algebras, all physical structures can be interpreted in terms of corresponding realizations or representations. Physical properties are related eigenvalues or invariants. As an explicit example of operational spacetime is proposed, called electroweak spacetime, parametrizing the classes of the internal hypercharge - isospin group in the general linear group in two complex dimensions, i.e., the Lorentz cover group, extended by the casual (dilation) and phase group. Its representations and invariants will be investigated with the aim to connect them, qualitatively and numerically, with the properties of interactions and particles as arising in the representations of its tangent Minkowski spaces.

Mental Representation Theory in Old French Allegory from the Twelfth and Thirteenth Centuries

Katharine G. MacCornack
Mental Representation Theory in Old French Allegory from the Twelfth and Thirteenth Centuries Book PDF

Author : Katharine G. MacCornack
Publisher : Unknown
Page : 252 pages
File Size : 46,8 Mb
Release : 1996
Category : History
ISBN : STANFORD:36105019222277

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Mental Representation Theory in Old French Allegory from the Twelfth and Thirteenth Centuries by Katharine G. MacCornack Pdf

This study uses mental representation theory, (propounded by Umberto Eco and other contemporary scholars) to interpret dream allegory in medieval French allegorical texts. The texts covered include The Romance of the Rose, The Dream of Hell, and The Tournament of the Antichrist. Mental representation theory interprets interpretation in a clearer, more complete fashion, by looking at the dream, the cosmic nature of allegory, and its linguistic and mental structures.

The Search for Certainty

Frank J. Swetz
The Search for Certainty Book PDF

Author : Frank J. Swetz
Publisher : Courier Corporation
Page : 194 pages
File Size : 53,8 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486474427

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The Search for Certainty by Frank J. Swetz Pdf

Self-contained and authoritative, this history of mathematics is suited to those with no math background. Its absorbing, entertaining essays focus on the era from 1800 to 2000. Contributors include Henri Poincaré, Judith V. Grabiner, and H. S. M. Coxeter, who discuss topics ranging from logic and infinity to Fermat's Last Theorem.