Introduction to the Representation Theory of Compact and Locally Compact Groups

Introduction to the Representation Theory of Compact and Locally Compact Groups
Author: Alain Robert
Publisher: Cambridge University Press
Total Pages: 217
Release: 1983-02-10
Genre: Mathematics
ISBN: 0521289750

Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Induced Representations of Locally Compact Groups

Induced Representations of Locally Compact Groups
Author: Eberhard Kaniuth
Publisher: Cambridge University Press
Total Pages: 359
Release: 2013
Genre: Mathematics
ISBN: 052176226X

A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

A Course in Abstract Harmonic Analysis

A Course in Abstract Harmonic Analysis
Author: Gerald B. Folland
Publisher: CRC Press
Total Pages: 317
Release: 2016-02-03
Genre: Mathematics
ISBN: 1498727158

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

Introduction to the Theory of Banach Representations of Groups

Introduction to the Theory of Banach Representations of Groups
Author: Yurii I. Lyubich
Publisher: Birkhäuser
Total Pages: 231
Release: 2012-12-06
Genre: Science
ISBN: 3034891695

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.

Lie Algebras and Locally Compact Groups

Lie Algebras and Locally Compact Groups
Author: Irving Kaplansky
Publisher: University of Chicago Press
Total Pages: 161
Release: 1971
Genre: Mathematics
ISBN: 0226424537

This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Representations of Compact Lie Groups

Representations of Compact Lie Groups
Author: T. Bröcker
Publisher: Springer Science & Business Media
Total Pages: 323
Release: 2013-03-14
Genre: Mathematics
ISBN: 3662129183

This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

Linear Analysis and Representation Theory

Linear Analysis and Representation Theory
Author: Steven A. Gaal
Publisher: Springer Science & Business Media
Total Pages: 701
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642807410

In an age when more and more items. are made to be quickly disposable or soon become obsolete due to either progress or other man caused reasons it seems almost anachronistic to write a book in the classical sense. A mathematics book becomes an indespensible companion, if it is worthy of such a relation, not by being rapidly read from cover to cover but by frequent browsing, consultation and other occasional use. While trying to create such a work I tried not to be encyclopedic but rather select only those parts of each chosen topic which I could present clearly and accurately in a formulation which is likely to last. The material I chose is all mathematics which is interesting and important both for the mathematician and to a large extent also for the mathematical physicist. I regret that at present I could not give a similar account on direct integrals and the representation theory of certain classes of Lie groups. I carefully kept the level of presentation throughout the whole book as uniform as possible. Certain introductory sections are kept shorter and are perhaps slightly more detailed in order to help the newcomer prog ress with it at the same rate as the more experienced person is going to proceed with his study of the details.