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Locally Compact Groups

Stroppel, Markus,

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Locally Compact Groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Locally Compact Groups/ Markus Stroppel
Author:	Stroppel, Markus,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2006,
Description:	1 online resource (312 pages)
Subject:	Groups & group theory -
Online resource:	https://doi.org/10.4171/016
Online resource:	https://www.ems-ph.org/img/books/stroppel_mini.jpg
ISBN:	9783037195161

Locally Compact Groups
Stroppel, Markus,

Locally Compact Groups[electronic resource] /Markus Stroppel - Zuerich, Switzerland :European Mathematical Society Publishing House,2006 - 1 online resource (312 pages) - EMS Textbooks in Mathematics (ETB).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.

ISBN: 9783037195161

Standard No.: 10.4171/016doiSubjects--Topical Terms:

3480852
Groups & group theory

Locally Compact Groups
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520 $a Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.
650 0 7 $a Groups & group theory $2 bicssc $3 3480852
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650 0 7 $a Field theory and polynomials $2 msc $3 3480819
650 0 7 $a Group theory and generalizations $2 msc $3 3480853
650 0 7 $a Abstract harmonic analysis $2 msc $3 3480854
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