Invariant Subsemigroups Of Lie Groups

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Invariant Subsemigroups of Lie Groups

Karl-Hermann Neeb
Invariant Subsemigroups of Lie Groups Book PDF

Author : Karl-Hermann Neeb
Publisher : American Mathematical Soc.
Page : 193 pages
File Size : 49,8 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825624

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Invariant Subsemigroups of Lie Groups by Karl-Hermann Neeb Pdf

This work presents the first systematic treatment of invariant Lie semi groups. Because these semi groups provide interesting models for space times in general relativity, this work will be useful to both mathematicians and physicists. It will also appeal to engineers interested in bi-invariant control systems on Lie groups. Neeb investigates closed invariant subsemigroups of Lie groups which are generated by one-parameter semi groups and the sets of infinitesimal generators of such semi groups - invariant convex cones in Lie algebras.In addition, a characterization of those finite-dimensional real Lie algebras containing such cones is obtained. The global part of the theory deals with globality problems (Lie's third theorem for semi groups), controllability problems, and the facial structure of Lie semi groups. Neeb also determines the structure of the universal compactification of an invariant Lie semigroup and shows that the lattice of idempotents is isomorphic to a lattice of faces of the cone dual to the cone of infinitesimal generators.

Lie Semigroups and their Applications

Joachim Hilgert,Karl-Hermann Neeb
Lie Semigroups and their Applications Book PDF

Author : Joachim Hilgert,Karl-Hermann Neeb
Publisher : Springer
Page : 327 pages
File Size : 53,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540699873

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Lie Semigroups and their Applications by Joachim Hilgert,Karl-Hermann Neeb Pdf

Subsemigroups of finite-dimensional Lie groups that are generated by one-parameter semigroups are the subject of this book. It covers basic Lie theory for such semigroups and some closely related topics. These include ordered homogeneous manifolds, where the order is defined by a field of cones, invariant cones in Lie algebras and associated Ol'shanskii semigroups. Applications to representation theory, symplectic geometry and Hardy spaces are also given. The book is written as an efficient guide for those interested in subsemigroups of Lie groups and their applications in various fields of mathematics (see the User's guide at the end of the Introduction). Since it is essentially self-contained and leads directly to the core of the theory, the first part of the book can also serve as an introduction to the subject. The reader is merely expected to be familiar with the basic theory of Lie groups and Lie algebras.

Lie Groups, Convex Cones, and Semigroups

Joachim Hilgert,Karl Heinrich Hofmann,Jimmie D. Lawson
Lie Groups Convex Cones and Semigroups Book PDF

Author : Joachim Hilgert,Karl Heinrich Hofmann,Jimmie D. Lawson
Publisher : Oxford University Press, USA
Page : 696 pages
File Size : 43,9 Mb
Release : 1989
Category : Law
ISBN : UCAL:B4360092

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Lie Groups, Convex Cones, and Semigroups by Joachim Hilgert,Karl Heinrich Hofmann,Jimmie D. Lawson Pdf

This is the first and only reference to provide a comprehensive treatment of the Lie theory of subsemigroups of Lie groups. The book is uniquely accessible and requires little specialized knowledge. It includes information on the infinitesimal theory of Lie subsemigroups, and a characterization of those cones in a Lie algebra which are invariant under the action of the group of inner automporphisms. It provides full treatment of the local Lie theory for semigroups, and finally, gives the reader a useful account of the global theory for the existence of subsemigroups with a given set of infinitesimal generators.

Lie Groups and Subsemigroups with Surjective Exponential Function

Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Lie Groups and Subsemigroups with Surjective Exponential Function Book PDF

Author : Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 40,7 Mb
Release : 1997
Category : Exponential functions
ISBN : 9780821806418

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Lie Groups and Subsemigroups with Surjective Exponential Function by Karl Heinrich Hofmann,Wolfgang Ruppert,Wolfgang A. F. Ruppert Pdf

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

Probability on Algebraic Structures

Gregory Budzban,Arunava Mukherjea
Probability on Algebraic Structures Book PDF

Author : Gregory Budzban,Arunava Mukherjea
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 54,8 Mb
Release : 2000
Category : Lie groups
ISBN : 9780821820278

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Probability on Algebraic Structures by Gregory Budzban,Arunava Mukherjea Pdf

This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.

Semigroups in Algebra, Geometry and Analysis

Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg
Semigroups in Algebra Geometry and Analysis Book PDF

Author : Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg
Publisher : Walter de Gruyter
Page : 385 pages
File Size : 54,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110885583

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Semigroups in Algebra, Geometry and Analysis by Karl H. Hofmann,Jimmie D. Lawson,Ernest B. Vinberg Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Holomorphy and Convexity in Lie Theory

Karl-Hermann Neeb
Holomorphy and Convexity in Lie Theory Book PDF

Author : Karl-Hermann Neeb
Publisher : Walter de Gruyter
Page : 804 pages
File Size : 43,6 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110808148

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Holomorphy and Convexity in Lie Theory by Karl-Hermann Neeb Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Positivity in Lie Theory

Joachim Hilgert,Jimmie D. Lawson,Karl-Hermann Neeb,Ernest B. Vinberg
Positivity in Lie Theory Book PDF

Author : Joachim Hilgert,Jimmie D. Lawson,Karl-Hermann Neeb,Ernest B. Vinberg
Publisher : Walter de Gruyter
Page : 305 pages
File Size : 50,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110811186

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Positivity in Lie Theory by Joachim Hilgert,Jimmie D. Lawson,Karl-Hermann Neeb,Ernest B. Vinberg Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Lectures on Gaussian Integral Operators and Classical Groups

Yu. A. Neretin
Lectures on Gaussian Integral Operators and Classical Groups Book PDF

Author : Yu. A. Neretin
Publisher : European Mathematical Society
Page : 576 pages
File Size : 43,7 Mb
Release : 2011
Category : Geometry, Differential
ISBN : 3037190809

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Lectures on Gaussian Integral Operators and Classical Groups by Yu. A. Neretin Pdf

This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.

Reflection Positivity

Karl-Hermann Neeb,Gestur Ólafsson
Reflection Positivity Book PDF

Author : Karl-Hermann Neeb,Gestur Ólafsson
Publisher : Springer
Page : 139 pages
File Size : 40,8 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.

Lie Theory and Its Applications in Physics

H-D Doebner,J Hilgert,V K Dobrev
Lie Theory and Its Applications in Physics Book PDF

Author : H-D Doebner,J Hilgert,V K Dobrev
Publisher : World Scientific
Page : 284 pages
File Size : 54,7 Mb
Release : 1996-10-16
Category : Electronic
ISBN : 9789814547086

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Lie Theory and Its Applications in Physics by H-D Doebner,J Hilgert,V K Dobrev Pdf

There is an apparent trend towards geometrization of physical theories. During the last 20 years, the most successful mathematical models for the description and understanding of physical systems have been based on the Lie theory in its widest sense and various generalizations, for example, deformations of it. This proceedings volume reflects part of the development. On the mathematical side, they report on representations of Lie algebras, quantization procedures, non-commutative geometry, quantum groups, etc. Furthermore, possible physical applications of these techniques are discussed (e.g. quantization of classical systems, derivations of evolution equations, discrete and deformed physical systems). This volume complements the book Generalized Symmetries in Physics, published by World Scientific in 1994. Contents:Representation Theory and Quantization MethodsNoncommutative Geometry, Quantum Algebras and Applications to Relativistic and Nonrelativistic SystemsSpecial Applications to Physical Systems and Their Generalized ModelsRepresentation Theory and Quantization Methods Readership: Mathematicians and physicists. keywords:

Finite Rational Matrix Groups

Gabriele Nebe,Wilhelm Plesken
Finite Rational Matrix Groups Book PDF

Author : Gabriele Nebe,Wilhelm Plesken
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 55,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803431

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Finite Rational Matrix Groups by Gabriele Nebe,Wilhelm Plesken Pdf

The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and $p+1$ and $p-1$ for all prime numbers $p$. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.

Weyl Groups and Birational Transformations Among Minimal Models

Kenji Matsuki
Weyl Groups and Birational Transformations Among Minimal Models Book PDF

Author : Kenji Matsuki
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 45,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803417

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Weyl Groups and Birational Transformations Among Minimal Models by Kenji Matsuki Pdf

This work provides a unified way of looking at the apparently sporadic Weyl groups connected with the classical algebraic geometry of surfaces from the viewpoint of the recently established Minimal Model Program for $3$-folds (Mori's Program). Matsuki explores the correspondence between the algebraic objects (the Weyl chambers, roots, reflections) and geometric objects (the ample cones of minimal models, extremal rays, flops) for the Weyl groups appearing with rational double points, Kodaira-type degenerations of elliptic curves and K3 surfaces. A complete table for all the extremal rays of Fano $3$-folds also appears here for the first time, along with some interesting examples of flops for $4$-folds.

Unraveling the Integral Knot Concordance Group

Neal W. Stoltzfus
Unraveling the Integral Knot Concordance Group Book PDF

Author : Neal W. Stoltzfus
Publisher : American Mathematical Soc.
Page : 91 pages
File Size : 54,9 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821821923

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Unraveling the Integral Knot Concordance Group by Neal W. Stoltzfus Pdf

The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.

Manifolds with Group Actions and Elliptic Operators

Vladimir I͡Akovlevich Lin,Yehuda Pinchover
Manifolds with Group Actions and Elliptic Operators Book PDF

Author : Vladimir I͡Akovlevich Lin,Yehuda Pinchover
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 53,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821826041

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Manifolds with Group Actions and Elliptic Operators by Vladimir I͡Akovlevich Lin,Yehuda Pinchover Pdf

This work studies equivariant linear second order elliptic operators P on a connected noncompact manifold X with a given action of a group G . The action is assumed to be cocompact, meaning that GV=X for some compact subset V of X . The aim is to study the structure of the convex cone of all positive solutions of Pu= 0. It turns out that the set of all normalized positive solutions which are also eigenfunctions of the given G -action can be realized as a real analytic submanifold *G [0 of an appropriate topological vector space *H . When G is finitely generated, *H has finite dimension, and in nontrivial cases *G [0 is the boundary of a strictly convex body in *H. When G is nilpotent, any positive solution u can be represented as an integral with respect to some uniquely defined positive Borel measure over *G [0 . Lin and Pinchover also discuss related results for parabolic equations on X and for elliptic operators on noncompact manifolds with boundary.