The Structure of Compact Groups : : A Primer for the Student – A Handbook for the Expert / / Karl H. Hofmann, Sidney A. Morris.
The subject matter of compact groups is frequently cited in fi elds like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a text for upper level graduate students, and of being a source book for researchers who need the structure and rep...
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Hofmann, Karl H., author. aut http://id.loc.gov/vocabulary/relators/aut The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / Karl H. Hofmann, Sidney A. Morris. Berlin ; Boston : De Gruyter, [2023] ©2023 1 online resource (XLI, 1032 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Studies in Mathematics , 0179-0986 ; 25 Frontmatter -- Preface to the Fifth Edition -- Highlights of the Structure Theory of Compact Groups -- Preface to the Fourth Edition -- Preface to the Second and Third Editions -- Preface to the First Edition -- Contents -- Chapter 1. Basic Topics and Examples -- Chapter 2. The Basic Representation Theory of Compact Groups -- Chapter 3. The Ideas of Peter & Weyl, Tannaka, Hopf, & Hochschild -- Chapter 4. Characters -- Chapter 5. Linear Lie Groups -- Chapter 6. Compact Lie Groups -- Chapter 7. Duality of Abelian Topological Groups -- Chapter 8. Compact Abelian Groups -- Chapter 9. The Structure of Compact Groups -- Chapter 10. Compact Group Actions -- Chapter 11. The Structure of Free Compact Groups -- Chapter 12. Cardinal Invariants of Compact Groups -- Appendix 1. Abelian Groups -- Appendix 2. Covering Spaces and Groups -- Appendix 3. A Primer of Category Theory -- Appendix 4. Selected Results on Topology and Topological Groups -- Appendix 5. Measures on Compact Groups -- Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups -- Appendix 7. Weakly Complete Vector Spaces and Algebras -- References -- Index of Symbols -- Index -- De Gruyter Studies in Mathematics restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The subject matter of compact groups is frequently cited in fi elds like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a text for upper level graduate students, and of being a source book for researchers who need the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups and on locally compact abelian groups.Appended chapters contain the material for self-contained courses on abelian groups and on category theory.Using the Lie algebras and the exponential function of arbitrary compact groups, the book avoids unnecessary restrictions to finite dimensional or abelian compact groups. Earlier editions of 1998, 2006, 2013, and 2020 have been "ed for instruction and research. The present edition conceptually sharpens, polishes, and improves the earlier material. For instance, it includes a treatment of the Bohr compactifi cation of topological groups which fi ts perfectly into the general treatment of adjoint functors that the book treats in an appendix of its own, and which, in the abelian environment, connects neatly with the Pontryagin--van Kampen duality of compact abelian groups having been discussed in the book in great detail. The link between arbitrary compact groups and their weakly complete group algebras is as extensively discussed as is now the theory of weakly complete universal enveloping algebras of the Lie algebras of compact groups. All of this is based on the category of weakly complete real and complex vector spaces and its precise duality to the category of ordinary real, respectively, complex vector spaces, is treated in an appendix systematically. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Jun 2024) Abelsche Gruppen. Kategorientheorie. Kompakte Gruppen. Luge Algebra. Topologische Gruppen. MATHEMATICS / Algebra / General. bisacsh Abelian groups, category theory, compact groups, Lie algebra, topological groups. Morris, Sidney A., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 9783111175782 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 English 9783111319292 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2023 9783111318912 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 English 9783111319209 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2023 9783111318608 ZDB-23-DMA EPUB 9783111174051 print 9783111171630 https://doi.org/10.1515/9783111172606 https://www.degruyter.com/isbn/9783111172606 Cover https://www.degruyter.com/document/cover/isbn/9783111172606/original |
language |
English |
format |
eBook |
author |
Hofmann, Karl H., Hofmann, Karl H., Morris, Sidney A., |
spellingShingle |
Hofmann, Karl H., Hofmann, Karl H., Morris, Sidney A., The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / De Gruyter Studies in Mathematics , Frontmatter -- Preface to the Fifth Edition -- Highlights of the Structure Theory of Compact Groups -- Preface to the Fourth Edition -- Preface to the Second and Third Editions -- Preface to the First Edition -- Contents -- Chapter 1. Basic Topics and Examples -- Chapter 2. The Basic Representation Theory of Compact Groups -- Chapter 3. The Ideas of Peter & Weyl, Tannaka, Hopf, & Hochschild -- Chapter 4. Characters -- Chapter 5. Linear Lie Groups -- Chapter 6. Compact Lie Groups -- Chapter 7. Duality of Abelian Topological Groups -- Chapter 8. Compact Abelian Groups -- Chapter 9. The Structure of Compact Groups -- Chapter 10. Compact Group Actions -- Chapter 11. The Structure of Free Compact Groups -- Chapter 12. Cardinal Invariants of Compact Groups -- Appendix 1. Abelian Groups -- Appendix 2. Covering Spaces and Groups -- Appendix 3. A Primer of Category Theory -- Appendix 4. Selected Results on Topology and Topological Groups -- Appendix 5. Measures on Compact Groups -- Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups -- Appendix 7. Weakly Complete Vector Spaces and Algebras -- References -- Index of Symbols -- Index -- De Gruyter Studies in Mathematics |
author_facet |
Hofmann, Karl H., Hofmann, Karl H., Morris, Sidney A., Morris, Sidney A., Morris, Sidney A., |
author_variant |
k h h kh khh k h h kh khh s a m sa sam |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Morris, Sidney A., Morris, Sidney A., |
author2_variant |
s a m sa sam |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Hofmann, Karl H., |
title |
The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / |
title_sub |
A Primer for the Student – A Handbook for the Expert / |
title_full |
The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / Karl H. Hofmann, Sidney A. Morris. |
title_fullStr |
The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / Karl H. Hofmann, Sidney A. Morris. |
title_full_unstemmed |
The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / Karl H. Hofmann, Sidney A. Morris. |
title_auth |
The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / |
title_alt |
Frontmatter -- Preface to the Fifth Edition -- Highlights of the Structure Theory of Compact Groups -- Preface to the Fourth Edition -- Preface to the Second and Third Editions -- Preface to the First Edition -- Contents -- Chapter 1. Basic Topics and Examples -- Chapter 2. The Basic Representation Theory of Compact Groups -- Chapter 3. The Ideas of Peter & Weyl, Tannaka, Hopf, & Hochschild -- Chapter 4. Characters -- Chapter 5. Linear Lie Groups -- Chapter 6. Compact Lie Groups -- Chapter 7. Duality of Abelian Topological Groups -- Chapter 8. Compact Abelian Groups -- Chapter 9. The Structure of Compact Groups -- Chapter 10. Compact Group Actions -- Chapter 11. The Structure of Free Compact Groups -- Chapter 12. Cardinal Invariants of Compact Groups -- Appendix 1. Abelian Groups -- Appendix 2. Covering Spaces and Groups -- Appendix 3. A Primer of Category Theory -- Appendix 4. Selected Results on Topology and Topological Groups -- Appendix 5. Measures on Compact Groups -- Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups -- Appendix 7. Weakly Complete Vector Spaces and Algebras -- References -- Index of Symbols -- Index -- De Gruyter Studies in Mathematics |
title_new |
The Structure of Compact Groups : |
title_sort |
the structure of compact groups : a primer for the student – a handbook for the expert / |
series |
De Gruyter Studies in Mathematics , |
series2 |
De Gruyter Studies in Mathematics , |
publisher |
De Gruyter, |
publishDate |
2023 |
physical |
1 online resource (XLI, 1032 p.) Issued also in print. |
contents |
Frontmatter -- Preface to the Fifth Edition -- Highlights of the Structure Theory of Compact Groups -- Preface to the Fourth Edition -- Preface to the Second and Third Editions -- Preface to the First Edition -- Contents -- Chapter 1. Basic Topics and Examples -- Chapter 2. The Basic Representation Theory of Compact Groups -- Chapter 3. The Ideas of Peter & Weyl, Tannaka, Hopf, & Hochschild -- Chapter 4. Characters -- Chapter 5. Linear Lie Groups -- Chapter 6. Compact Lie Groups -- Chapter 7. Duality of Abelian Topological Groups -- Chapter 8. Compact Abelian Groups -- Chapter 9. The Structure of Compact Groups -- Chapter 10. Compact Group Actions -- Chapter 11. The Structure of Free Compact Groups -- Chapter 12. Cardinal Invariants of Compact Groups -- Appendix 1. Abelian Groups -- Appendix 2. Covering Spaces and Groups -- Appendix 3. A Primer of Category Theory -- Appendix 4. Selected Results on Topology and Topological Groups -- Appendix 5. Measures on Compact Groups -- Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups -- Appendix 7. Weakly Complete Vector Spaces and Algebras -- References -- Index of Symbols -- Index -- De Gruyter Studies in Mathematics |
isbn |
9783111172606 9783111175782 9783111319292 9783111318912 9783111319209 9783111318608 9783111174051 9783111171630 |
issn |
0179-0986 ; |
url |
https://doi.org/10.1515/9783111172606 https://www.degruyter.com/isbn/9783111172606 https://www.degruyter.com/document/cover/isbn/9783111172606/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512/.55 |
dewey-sort |
3512 255 |
dewey-raw |
512/.55 |
dewey-search |
512/.55 |
doi_str_mv |
10.1515/9783111172606 |
oclc_num |
1408681982 |
work_keys_str_mv |
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ids_txt_mv |
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The Structure of Compact Groups : A Primer for the Student – A Handbook for the Expert / |
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