Deformation Quantization of Some Non-compact Solvable Lie Groups and Their Representation Theory PDF Download

Author: Byung-Jay Kahng
Publisher:
ISBN:
Category :
Languages : en
Pages : 308

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Author: Didier Arnal
Publisher: Cambridge University Press
ISBN: 1108651933
Category : Mathematics
Languages : en
Pages : 464

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Book Description
The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.

Author: Howard D Fegan
Publisher: World Scientific Publishing Company
ISBN: 9813103469
Category :
Languages : en
Pages : 147

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Book Description
There are two approaches to compact lie groups: by computation as matrices or theoretically as manifolds with a group structure. The great appeal of this book is the blending of these two approaches. The theoretical results are illustrated by computations and the theory provides a commentary on the computational work. Indeed, there are extensive computations of the structure and representation theory for the classical groups SU(n), SO(n) and Sp(n). A second exciting feature is that the differential geometry of a compact Lie group, both the classical curvature studies and the more recent heat equation methods, are treated. A large number of formulas for the connection and curvature are conveniently gathered together.This book provides an excellent text for a first course in compact Lie groups.

Author: Louis Auslander
Publisher:
ISBN:
Category : Lie groups
Languages : en
Pages : 199

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Book Description
In this monograph, we are going to treat some aspects of the unitary representation theory of solvable Lie groups. One of the fundamental questions one can raise about any locally compact group or C* algebra is that of determining when it is type I and to try to determine the structure of the set of equivalence classes of its irreducible representations. It is this and closely related questions which will occupy us here. In the course of this investigation, we will have to make use of a rather elaborate theory of infinite dimensional unitary representations of groups and algebras, and have thus included a rather lengthly expository introduction.

Author: V.V. Gorbatsevich
Publisher: Springer Science & Business Media
ISBN: 364257999X
Category : Mathematics
Languages : en
Pages : 241

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From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

Author: Carolyn Gordon
Publisher: American Mathematical Soc.
ISBN: 0821846515
Category : Mathematics
Languages : en
Pages : 363

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Book Description
This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.

Author: Sergei D. Silvestrov
Publisher: Springer Science & Business Media
ISBN: 3540853324
Category : Mathematics
Languages : en
Pages : 308

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Book Description
This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.

Author: Gilles Halbout
Publisher: Walter de Gruyter
ISBN: 3110866226
Category : Mathematics
Languages : en
Pages : 244

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Book Description
This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001. Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.

Author: Ali Baklouti
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311076539X
Category : Mathematics
Languages : en
Pages : 379

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This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

Author: Dmitriĭ Petrovich Zhelobenko
Publisher:
ISBN: 9781470444556
Category : Lie groups
Languages : en
Pages : 461

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Book Description
The content of this book is somewhat different from that of traditional books on representation theory. First, bearing in mind the needs of physicists, the author has tried to make the exposition as elementary as possible. The need for an elementary exposition has influenced the distribution of the material. The book is divided into three largely independent parts, arranged in order of increasing difficulty. Besides compact Lie groups, groups with other topological structure (""similar"" to compact groups in some sense) are considered. Prominent among these are reductive complex Lie groups (in.