Hofmann, Karl Heinrich
Overview
Works:  207 works in 753 publications in 8 languages and 10,948 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Illustrator, Editor, Redactor, Other 
Classifications:  QA3, 510 
Publication Timeline
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Most widely held works about
Karl Heinrich Hofmann
 Poster cartoons, 19831998 : posters by Karl Heinrich Hofmann( Book )
Most widely held works by
Karl Heinrich Hofmann
The structure of compact groups : a primer for the student, a handbook for the expert by
Karl Heinrich Hofmann(
Book
)
42 editions published between 1998 and 2013 in English and German and held by 478 WorldCat member libraries worldwide
Deals with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book is suitable for upper level graduate courses or seminars. It is useful for research specialists who need to apply the structure and representation theory of compact groups
42 editions published between 1998 and 2013 in English and German and held by 478 WorldCat member libraries worldwide
Deals with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book is suitable for upper level graduate courses or seminars. It is useful for research specialists who need to apply the structure and representation theory of compact groups
Compact semitopological semigroups and weakly almost periodic functions by
John F Berglund(
Book
)
30 editions published between 1967 and 2007 in 4 languages and held by 448 WorldCat member libraries worldwide
30 editions published between 1967 and 2007 in 4 languages and held by 448 WorldCat member libraries worldwide
The duality of compact semigroups and C*bigebras by
Karl Heinrich Hofmann(
Book
)
24 editions published between 1970 and 2008 in English and held by 437 WorldCat member libraries worldwide
24 editions published between 1970 and 2008 in English and held by 437 WorldCat member libraries worldwide
Elements of compact semigroups by
Karl Heinrich Hofmann(
Book
)
16 editions published in 1966 in English and Italian and held by 420 WorldCat member libraries worldwide
16 editions published in 1966 in English and Italian and held by 420 WorldCat member libraries worldwide
The Pontryagin duality of compact Odimensional semilattices and its applications by
Karl Heinrich Hofmann(
Book
)
24 editions published between 1974 and 2008 in English and Undetermined and held by 412 WorldCat member libraries worldwide
24 editions published between 1974 and 2008 in English and Undetermined and held by 412 WorldCat member libraries worldwide
Recent developments in the algebraic, analytical, and topological theory of semigroups : proceedings of a conference, held
at Oberwolfach, Germany, May 2430, 1981 by
Karl Heinrich Hofmann(
Book
)
23 editions published between 1981 and 1983 in 3 languages and held by 395 WorldCat member libraries worldwide
23 editions published between 1981 and 1983 in 3 languages and held by 395 WorldCat member libraries worldwide
Cohomology theories for compact Abelian groups by
Karl Heinrich Hofmann(
Book
)
25 editions published between 1973 and 2012 in English and German and held by 358 WorldCat member libraries worldwide
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
25 editions published between 1973 and 2012 in English and German and held by 358 WorldCat member libraries worldwide
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
Lie groups, convex cones, and semigroups by
Joachim Hilgert(
Book
)
9 editions published in 1989 in English and held by 300 WorldCat member libraries worldwide
9 editions published in 1989 in English and held by 300 WorldCat member libraries worldwide
Proofs from the book by
Martin Aigner(
Book
)
39 editions published between 1998 and 2014 in 4 languages and held by 300 WorldCat member libraries worldwide
This revised and enlarged fifth editionfeatures four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the nonexistence of the Borromean rings and other surprises. From the Reviews " ... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler ... write: " ... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ..." Notices of the AMS, August 1999 " ... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011
39 editions published between 1998 and 2014 in 4 languages and held by 300 WorldCat member libraries worldwide
This revised and enlarged fifth editionfeatures four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the nonexistence of the Borromean rings and other surprises. From the Reviews " ... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler ... write: " ... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ..." Notices of the AMS, August 1999 " ... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures, and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately, and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant, and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011
Crimes and mathdemeanors by
Leith Hathout(
Book
)
6 editions published between 2007 and 2010 in English and Korean and held by 256 WorldCat member libraries worldwide
Each chapter presents a new detective story with a mathematical puzzle at its core. Readers must test skills in mathematics and physics and enjoy Ravi's clever analysis of the intrigues using trigonometry, probability, combinatorics, deductive reasoning and wit
6 editions published between 2007 and 2010 in English and Korean and held by 256 WorldCat member libraries worldwide
Each chapter presents a new detective story with a mathematical puzzle at its core. Readers must test skills in mathematics and physics and enjoy Ravi's clever analysis of the intrigues using trigonometry, probability, combinatorics, deductive reasoning and wit
Continuous lattices and their applications(
Book
)
8 editions published in 1985 in English and held by 252 WorldCat member libraries worldwide
8 editions published in 1985 in English and held by 252 WorldCat member libraries worldwide
Lie groups and subsemigroups with surjective exponential function by
Karl Heinrich Hofmann(
Book
)
15 editions published between 1997 and 1998 in English and held by 245 WorldCat member libraries worldwide
15 editions published between 1997 and 1998 in English and held by 245 WorldCat member libraries worldwide
Semigroup theory and its applications : proceedings of the 1994 conference commemorating the work of Alfred H. Clifford by
Karl Heinrich Hofmann(
Book
)
18 editions published between 1996 and 2003 in English and held by 241 WorldCat member libraries worldwide
The Relationship of Al Clifford's Work to the Current Theory of SemigroupsReferences; Bands of Semigroups: Variations on a Clifford Theme; Introduction; 0. Green's Quasi Orders on Bands; 1. Bilateral Bands; 2. Proper Bands; 3. Further Corollaries; References; Isbell's Zigzag Theorem and its Consequences; 0. Introduction; 1. Epimorphism and Dominions; 2. Consequences; 3. Amalgamation; References; Part 3: New Results and Directions; On the Maps Implicit in the JordanHölder Theorem; 1. Introduction; 2. The Lattice of Subnormal Subgroups; 3. Semimodular Lattices; 4. The M3 Configuration
18 editions published between 1996 and 2003 in English and held by 241 WorldCat member libraries worldwide
The Relationship of Al Clifford's Work to the Current Theory of SemigroupsReferences; Bands of Semigroups: Variations on a Clifford Theme; Introduction; 0. Green's Quasi Orders on Bands; 1. Bilateral Bands; 2. Proper Bands; 3. Further Corollaries; References; Isbell's Zigzag Theorem and its Consequences; 0. Introduction; 1. Epimorphism and Dominions; 2. Consequences; 3. Amalgamation; References; Part 3: New Results and Directions; On the Maps Implicit in the JordanHölder Theorem; 1. Introduction; 2. The Lattice of Subnormal Subgroups; 3. Semimodular Lattices; 4. The M3 Configuration
Recent advances in the representation theory of rings and C*algebras by continuous sections; a seminar held at Tulane University,
New Orleans, Louisiana, March 28April 5, 1973 by
Karl Heinrich Hofmann(
Book
)
21 editions published in 1974 in English and held by 227 WorldCat member libraries worldwide
21 editions published in 1974 in English and held by 227 WorldCat member libraries worldwide
A general character theory for partially ordered sets and lattices by
Karl Heinrich Hofmann(
Book
)
15 editions published between 1972 and 2012 in English and Italian and held by 224 WorldCat member libraries worldwide
15 editions published between 1972 and 2012 in English and Italian and held by 224 WorldCat member libraries worldwide
Representation of rings by sections by
John Dauns(
Book
)
16 editions published between 1968 and 1983 in English and held by 212 WorldCat member libraries worldwide
16 editions published between 1968 and 1983 in English and held by 212 WorldCat member libraries worldwide
Splitting in topological groups by
Karl Heinrich Hofmann(
Book
)
21 editions published between 1963 and 1972 in 3 languages and held by 209 WorldCat member libraries worldwide
21 editions published between 1963 and 1972 in 3 languages and held by 209 WorldCat member libraries worldwide
The Lie theory of connected proLie groups : a structure theory for proLie algebras, proLie groups, and connected locally
compact groups by
Karl Heinrich Hofmann(
Book
)
12 editions published in 2007 in English and held by 146 WorldCat member libraries worldwide
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a proLie group. Every locally compact connected topological group and every compact group is a proLie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of proLie groups is. For half a century, locally compact proLie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of proLie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinitedimensional Lie groups. The results of this text are based on a theory of proLie algebras which parallels the structure theory of finitedimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected proLie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finitedimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics
12 editions published in 2007 in English and held by 146 WorldCat member libraries worldwide
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. If a complete topological group $G$ can be approximated by Lie groups in the sense that every identity neighborhood $U$ of $G$ contains a normal subgroup $N$ such that $G/N$ is a Lie group, then it is called a proLie group. Every locally compact connected topological group and every compact group is a proLie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of proLie groups is. For half a century, locally compact proLie groups have drifted through the literature, yet this is the first book which systematically treats the Lie and structure theory of proLie groups irrespective of local compactness. This study fits very well into the current trend which addresses infinitedimensional Lie groups. The results of this text are based on a theory of proLie algebras which parallels the structure theory of finitedimensional real Lie algebras to an astonishing degree, even though it has had to overcome greater technical obstacles. This book exposes a Lie theory of connected proLie groups (and hence of connected locally compact groups) and illuminates the manifold ways in which their structure theory reduces to that of compact groups on the one hand and of finitedimensional Lie groups on the other. It is a continuation of the authors' fundamental monograph on the structure of compact groups (1998, 2006) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis, and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of current research, which has so many fruitful interactions with other fields of mathematics
Symmetry of discrete mathematical structures and their symmetry groups : a collection of essays(
Book
)
10 editions published in 1991 in 3 languages and held by 128 WorldCat member libraries worldwide
10 editions published in 1991 in 3 languages and held by 128 WorldCat member libraries worldwide
The algebraic theory of compact Lawson semilattices : applications of Galois connections to compact semilattices by
Karl Heinrich Hofmann(
Book
)
9 editions published in 1976 in English and Polish and held by 70 WorldCat member libraries worldwide
9 editions published in 1976 in English and Polish and held by 70 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Morris, Sidney A. 1947 Other Author
 Mislove, Michael W. Other Author Editor
 Clifford, A. H. (Alfred Hoblitzelle) 1908 Other Honoree Editor
 Ziegler, Günter M.
 Aigner, Martin 1942 Author
 Stralka, Albert Author
 Weinert, Hanns Joachim Editor
 Jürgensen, Helmut Editor
 Berglund, John F. Author
 Mostert, Paul S. (Paul Stallings)
Useful Links
Associated Subjects
Abelian groups Algebra Almost periodic functions C*algebras Caricatures and cartoons Categories (Mathematics) Combinatorial analysis Compact Abelian groups Compact groups Computer science Cone Connections (Mathematics) Continuous lattices Convex bodies Detective and mystery stories Distribution (Probability theory) Duality theory (Mathematics) Exponential functions Fiber bundles (Mathematics) Galois theory Geometry Global analysis (Mathematics) Group theory Homology theory Lattice theory Lie algebras Lie groups Locally compact groups Loops (Group theory) Mathematical recreations Mathematics Number theory Ordered sets Partially ordered sets Pontrjagin duality Proof theory Reasoning Representations of algebras Representations of rings (Algebra) Rings (Algebra) Semigroups Semilattices Sheaf theory Symmetry Symmetry groups Topological groups Topological semigroups Topological spaces Topology Wedges
Alternative Names
Hofmann, K. H.
Hofmann, K. H. 1932
Hofmann, K. H. (Karl Heinrich)
Hofmann, Karl
Hofmann, Karl 1932
Hofmann, Karl H.
Hofmann, Karl H. (Karl Heinrich)
Hofmann, KarlHeinrich
Hofmann, KarlHeinrich 1932
Karl Heinrich Hofmann deutscher Mathematiker
Karl Heinrich Hofmann Duits wiskundige
Karl Heinrich Hofmann German mathematician
Languages
English
(349)
French (10)
German (9)
Italian (4)
Polish (3)
Multiple languages (1)
Miscellaneous languages (1)
Korean (1)
French (10)
German (9)
Italian (4)
Polish (3)
Multiple languages (1)
Miscellaneous languages (1)
Korean (1)
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