MARC Record from marc_columbia

LEADER: 03930cam a22005894a 4500
001 16273013
005 20220528225541.0
006 m o d
007 cr |n|||||||||
008 070703s2006 sz a ob 001 0 eng c
035 $a(OCoLC)ocn655713272
035 $a(NNC)16273013
040 $aCOO$beng$cCOO$dOCLCQ$dOCLCF$dOCLCO$dNOC$dOCLCQ$dLLB$dHEBIS$dOCLCO$dSTF$dINT$dOCLCQ$dOCLCA$dN$T$dOCLCO
019 $a1030562905
020 $a3037190167
020 $a9783037190166
020 $a3037195169
020 $a9783037195161$q(electronic bk.)
024 70 $a10.4171/016$2doi
035 $a(OCoLC)655713272$z(OCoLC)1030562905
042 $apcc
050 14 $aQA387$b.S77 2006
072 7 $aPBFD$2bicssc
082 04 $a512.55$223
084 $a22-xx$a12-xx$a20-xx$a43-xx$2msc
049 $aZCUA
100 1 $aStroppel, Markus.
245 10 $aLocally compact groups /$cMarkus Stroppel.
260 $aZürich, Switzerland :$bEuropean Mathematical Society,$c©2006.
300 $a1 online resource (x, 302 pages) :$billustrations.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aEMS textbooks in mathematics
504 $aIncludes bibliographical references (pages 287-290) and indexes.
505 0 $aTopological groups -- Topological transformation gropus -- The Haar integral -- Categories of topological groups -- Locally compact Abelian groups -- Locally compact semigroups -- Hilbert's fifth problem.
520 $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.
650 0 $aLocally compact groups.
650 6 $aGroupes localement compacts.
650 07 $aGroups & group theory.$2bicssc
650 7 $aLocally compact groups.$2fast$0(OCoLC)fst01001672
650 7 $aLokal kompakte Gruppe$2gnd
651 7 $aLokale Gruppe$2gnd
650 07 $aTopological groups, Lie groups.$2msc
650 07 $aField theory and polynomials.$2msc
650 07 $aGroup theory and generalizations.$2msc
650 07 $aAbstract harmonic analysis.$2msc
655 4 $aElectronic books.
830 0 $aEMS textbooks in mathematics.
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio16273013$zAll EBSCO eBooks
852 8 $blweb$hEBOOKS