03015nam a22003735a 450000100100000000300120001000500170002200600190003900700150005800800410007302000180011402400210013204000140015307200170016708400360018410000310022024500690025126000820032030000340040233600260043633700260046233800360048834700240052449000390054850600660058752016980065365000340235165000400238565000380242565000420246365000360250585600320254185600680257337-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20060228sz fot ||| 0|eng d a978303719516170a10.4171/0162doi ach0018173 7aPBFD2bicssc a22-xxa12-xxa20-xxa43-xx2msc1 aStroppel, Markus,eauthor.10aLocally Compact Groupsh[electronic resource] /cMarkus Stroppel3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2006 a1 online resource (312 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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 Peterâ€“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.07aGroups & group theory2bicssc07aTopological groups, Lie groups2msc07aField theory and polynomials2msc07aGroup theory and generalizations2msc07aAbstract harmonic analysis2msc40uhttps://doi.org/10.4171/016423cover imageuhttps://www.ems-ph.org/img/books/stroppel_mini.jpg