Karl H. Hofmann – författare

This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.

This book contains articles on the notion of a continuous lattice, which has its roots in Dana Scott's work on a mathematical theory of computation, presented at a conference on categorical and topological aspects of continuous lattices held in 1982.

No detailed description available for "The Analytical and Topological Theory of Semigroups".

No detailed description available for "Semigroups in Algebra, Geometry and Analysis".

Hellmuth Kneser (1898-1973) is the second of three mathematicians from consecutive generations of the Kneser family, all of them with groundbreaking mathematical contributions on a wide range of topics. It was only in recent times that mathematicians recognized how Hellmuth Kneser's work influenced the course of topology and the theory of several complex variables in the 20th century. Indeed he was a mathematician of extraordinarily broad vision and insight and thus contributed to many mathematical fields of pure and applied mathematics including foundations, differential equations, operations research, and mathematics education. With the exception of two papers written in French, all of his articles were written in German. Not all of them are readily available through the usual sources. For this book, presenting the entire collection of Kneser's papers published in journals, experts in various areas have written English commentaries on aspects of Hellmuth Kneser's work, summarizing what he accomplished, describing the context of his work, and giving outlooks on its aftereffects.

Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book – now in its third revised and augmented edition – has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply 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, on compact Lie groups, and on locally compact abelian groups. However, the thrust of book points in the direction of the structure theory of infinite dimensional, not necessarily commutative compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups.

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

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

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

No detailed description available for "e;The Analytical and Topological Theory of Semigroups"e;.

No detailed description available for "e;Semigroups in Algebra, Geometry and Analysis"e;.

Hellmuth Kneser (1898-1973) ist der Zweite von drei bedeutenden Mathematikern aus aufeinander folgenden Generationen der Familie Kneser, die wegweisende Erkenntnisse in einem erstaunlich breiten Spektrum von Spezialgebieten beisteuerten. Erst in jüngster Zeit haben Fachleute erkannt, wie sehr Hellmuth Knesers Arbeit die Entwicklung der Topologie und der Theorie mehrerer komplexer Variablen beeinflusst hat. Er war ein Mathematiker mit außerordentlichem Weitblick und hat daher auch wichtige Beiträge zu anderen Bereichen geleistet, darunter zur mathematischen Logik, zur Theorie der Differenzialgleichungen, zu den mathematischen Grundlagen der Wirtschaftswissenschaften (Operations Research) und zu den wissenschaftlichen Grundlagen der Schulmathematik. Die Arbeiten sind mit der Ausnahme von zwei in Französisch verfassten Artikeln in deutscher Sprache geschrieben.

Diese Werksammlung enthält alle in Zeitschriften veröffentlichten Arbeiten Knesers, sowie eine vollständige bislang unveröffentlichte Buchvorlage über seine Vorstellungen zur Schulmathematik. Sie enthält englische Kommentare von Spezialisten über verschiedene Aspekte des Kneserschen Werks mit Rückblicken, Analysen und Ausblicken.

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 quoted 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.

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 quoted 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.

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.