Karl H. Hofmann's Books

The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

By: Karl H. Hofmann,Sidney A. Morris

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The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

By: Karl H. Hofmann,Sidney A. Morris

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.

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1034

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110695995

ISBN 13

9783110695991

Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

By: Wolfgang Herfort,Karl H. Hofmann,Francesco G. Russo

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Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

By: Wolfgang Herfort,Karl H. Hofmann,Francesco G. Russo

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

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Page Count

358

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110599198

ISBN 13

9783110599190

Lie Groups and Subsemigroups with Surjective Exponential Function

By: Karl Heinrich Hofmann,Wolfgang Ruppert

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Lie Groups and Subsemigroups with Surjective Exponential Function

By: Karl Heinrich Hofmann,Wolfgang Ruppert

In the structure theory of real Lie groups, there is still information lacking about the exponential function. Most notably, there are no general necessary and sufficient conditions for the exponential function to be surjective. It is surprising that for subsemigroups of Lie groups, the question of the surjectivity of the exponential function can be answered. Under nature reductions setting aside the "group part" of the problem, subsemigroups of Lie groups with surjective exponential function are completely classified and explicitly constructed in this memoir. There are fewer than one would think and the proofs are harder than one would expect, requiring some innovative twists. The main protagonists on the scene are SL(2, R) and its universal covering group, almost abelian solvable Lie groups (ie. vector groups extended by homotheties), and compact Lie groups. This text will also be of interest to those working in algebra and algebraic geometry.

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Page Count

189

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806416

ISBN 13

9780821806418

Cohomology Theories for Compact Abelian Groups

By: Karl H. Hofmann,Paul S. Mostert

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Cohomology Theories for Compact Abelian Groups

By: Karl H. Hofmann,Paul S. Mostert

Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.

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Page Count

235

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642806708

ISBN 13

9783642806704

Book's by Karl H. Hofmann

The Structure of Compact Groups

The Structure of Compact Groups

Periodic Locally Compact Groups

Periodic Locally Compact Groups

Lie Groups and Subsemigroups with Surjective Exponential Function

Lie Groups and Subsemigroups with Surjective Exponential Function

Cohomology Theories for Compact Abelian Groups

Cohomology Theories for Compact Abelian Groups

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