Metric Geometry Of Locally Compact Groups

Author : Yves Cornulier
Publisher : European Mathematical Society
ISBN 13 : 9783037191668
Total Pages : 248 pages
Book Rating : 4.6X/5 ( download)

DOWNLOAD NOW!

Download or read book Metric Geometry of Locally Compact Groups written by Yves Cornulier and published by European Mathematical Society. This book was released on 2016 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups and can be favorably extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where ``coarse'' refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups. Basic results in the subject are exposed with complete proofs; others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as $p$-adic fields, isometry groups of various metric spaces, and last but not least, discrete groups themselves. The book is aimed at graduate students, advanced undergraduate students, and mathematicians seeking some introduction to coarse geometry and locally compact groups.

Author : Pierre-Emmanuel Caprace
Publisher : Cambridge University Press
ISBN 13 : 1108351948
Total Pages : 368 pages
Book Rating : 4.42/5 ( download)

DOWNLOAD NOW!

Download or read book New Directions in Locally Compact Groups written by Pierre-Emmanuel Caprace and published by Cambridge University Press. This book was released on 2018-02-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger–Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.

Author : Markus Stroppel
Publisher : European Mathematical Society
ISBN 13 : 9783037190166
Total Pages : 320 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book Locally Compact Groups written by Markus Stroppel and published by European Mathematical Society. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Pierre-Emmanuel Caprace
Publisher : Cambridge University Press
ISBN 13 : 1108413129
Total Pages : 367 pages
Book Rating : 4.21/5 ( download)

DOWNLOAD NOW!

Download or read book New Directions in Locally Compact Groups written by Pierre-Emmanuel Caprace and published by Cambridge University Press. This book was released on 2018-02-08 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Author : Wolfgang Herfort
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110599198
Total Pages : 354 pages
Book Rating : 4.90/5 ( download)

DOWNLOAD NOW!

Download or read book Periodic Locally Compact Groups written by Wolfgang Herfort and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups

Author : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424537
Total Pages : 161 pages
Book Rating : 4.38/5 ( download)

DOWNLOAD NOW!

Download or read book Lie Algebras and Locally Compact Groups written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Karl H. Hofmann
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110695995
Total Pages : 1034 pages
Book Rating : 4.91/5 ( download)

DOWNLOAD NOW!

Download or read book The Structure of Compact Groups written by Karl H. Hofmann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 1034 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.

Author : Eberhard Kaniuth
Publisher : Cambridge University Press
ISBN 13 : 052176226X
Total Pages : 359 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book Induced Representations of Locally Compact Groups written by Eberhard Kaniuth and published by Cambridge University Press. This book was released on 2013 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

Author : David Jordan
Publisher : Cambridge University Press
ISBN 13 : 1009103474
Total Pages : 408 pages
Book Rating : 4.73/5 ( download)

DOWNLOAD NOW!

Download or read book Modern Trends in Algebra and Representation Theory written by David Jordan and published by Cambridge University Press. This book was released on 2023-07-31 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Author : Christian Rosendal
Publisher : Cambridge University Press
ISBN 13 : 110884247X
Total Pages : 309 pages
Book Rating : 4.71/5 ( download)

DOWNLOAD NOW!

Download or read book Coarse Geometry of Topological Groups written by Christian Rosendal and published by Cambridge University Press. This book was released on 2021-12-16 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.