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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aLocally Compact Groups$b[electronic resource] /$fMarkus Stroppel
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2006
215   $a1 online resource (312 pages)
225 0 $aEMS Textbooks in Mathematics (ETB)
330   $aLocally 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.
606   $aGroups & group theory$2bicssc
606   $aTopological groups, Lie groups$2msc
606   $aField theory and polynomials$2msc
606   $aGroup theory and generalizations$2msc
606   $aAbstract harmonic analysis$2msc
615 07$aGroups & group theory
615 07$aTopological groups, Lie groups
615 07$aField theory and polynomials
615 07$aGroup theory and generalizations
615 07$aAbstract harmonic analysis
686   $a22-xx$a12-xx$a20-xx$a43-xx$2msc
700   $aStroppel$b Markus$0471646
801  0$bch0018173
906   $aBOOK
912   $a9910151937803321
996   $aLocally compact groups$9229409
997   $aUNINA