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Algebras And Their Automorphism Groups

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C Algebras and Their Automorphism Groups

C  Algebras and Their Automorphism Groups Book
Author : Søren Eilers,Dorte Olesen
Publisher : Academic Press
Release : 2018-08-08
ISBN : 0128141239
Language : En, Es, Fr & De

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Book Description :

This elegantly edited landmark edition of Gert Kjærgård Pedersen’s C*-Algebras and their Automorphism Groups (1979) carefully and sensitively extends the classic work to reflect the wealth of relevant novel results revealed over the past forty years. Revered from publication for its writing clarity and extremely elegant presentation of a vast space within operator algebras, Pedersen’s monograph is notable for reviewing partially ordered vector spaces and group automorphisms in unusual detail, and by strict intention releasing the C*-algebras from the yoke of representations as Hilbert space operators. Under the editorship of Søren Eilers and Dorte Olesen, the second edition modernizes Pedersen’s work for a new generation of C*-algebraists, with voluminous new commentary, all-new indexes, annotation and terminology annexes, and a surfeit of new discussion of applications and of the author’s later work. Covers basic C*-algebra theory in a short and appealingly elegant way, with a few additions and corrections given to the editors by the original author. Expands coverage to select contemporary accomplishments in C*-algebras of direct relevance to the scope of the first edition, including aspects of K-theory and set theory. Identifies key modern literature in an updated bibliography with over 100 new entries, and greatly enhances indexing throughout. Modernizes coverage of algebraic problems in relation to the theory of unitary representations of locally compact groups. Reviews mathematical accomplishments of Gert K. Pedersen in comments and a biography.

Theory of Operator Algebras II

Theory of Operator Algebras II Book
Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Release : 2002-11-01
ISBN : 9783540429142
Language : En, Es, Fr & De

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Book Description :

Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM

Generators and Relations in Groups and Geometries

Generators and Relations in Groups and Geometries Book
Author : A. Barlotti,E.W. Ellers,P. Plaumann,K. Strambach
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401133824
Language : En, Es, Fr & De

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Book Description :

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Theory of Operator Algebras I

Theory of Operator Algebras I Book
Author : M. Takesaki
Publisher : Springer Science & Business Media
Release : 2001-11-20
ISBN : 9783540422488
Language : En, Es, Fr & De

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Book Description :

Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.

Clifford Algebras and their Applications in Mathematical Physics

Clifford Algebras and their Applications in Mathematical Physics Book
Author : F. Brackx,R. Delanghe,H. Serras
Publisher : Springer Science & Business Media
Release : 1993-10-31
ISBN : 9780792323471
Language : En, Es, Fr & De

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Book Description :

This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.

The Minnesota Notes on Jordan Algebras and Their Applications

The Minnesota Notes on Jordan Algebras and Their Applications Book
Author : Max Koecher
Publisher : Springer Science & Business Media
Release : 1999-09-17
ISBN : 9783540663607
Language : En, Es, Fr & De

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Book Description :

This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.

Introduction to Vertex Operator Algebras and Their Representations

Introduction to Vertex Operator Algebras and Their Representations Book
Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Release : 2004
ISBN : 9780817634087
Language : En, Es, Fr & De

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Book Description :

The deep and relatively new field of vertex operator algebras is intimately related to a variety of areas in mathematics and physics: for example, the concepts of "monstrous moonshine," infinite-dimensional Lie theory, string theory, and conformal field theory. This book introduces the reader to the fundamental theory of vertex operator algebras and its basic techniques and examples. Beginning with a detailed presentation of the theoretical foundations and proceeding to a range of applications, the text includes a number of new, original results and also highlights and brings fresh perspective to important works of many researchers. After introducing the elementary "formal calculus'' underlying the subject, the book provides an axiomatic development of vertex operator algebras and their modules, expanding on the early contributions of R. Borcherds, I. Frenkel, J. Lepowsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu and others. The concept of a "representation'' of a vertex (operator) algebra is treated in detail, following and extending the work of H. Li; this approach is used to construct important families of vertex (operator) algebras and their modules. Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The booka??s presentation of the core topics will equip readers to embark on many active research directions related to vertex operator algebras, group theory, representation theory, and string theory.

Lectures on Real Semisimple Lie Algebras and Their Representations

Lectures on Real Semisimple Lie Algebras and Their Representations Book
Author : A. L. Onishchik
Publisher : European Mathematical Society
Release : 2004
ISBN : 9783037190029
Language : En, Es, Fr & De

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Book Description :

The book begins with a simplified (and somewhat extended and corrected) exposition of the main results of F. Karpelevich's 1955 paper and relates them to the theory of Cartan-Iwahori. It concludes with some tables, where an involution of the Dynkin diagram that allows for finding self-conjugate representations is described and explicit formulas for the index are given. In a short addendum, written by J. V. Silhan, this involution is interpreted in terms of the Satake diagram.

Exceptional Lie Algebras

Exceptional Lie Algebras Book
Author : N. Jacobson
Publisher : CRC Press
Release : 1971-06-01
ISBN : 9780824713263
Language : En, Es, Fr & De

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Book Description :

This volume presents a set of models for the exceptional Lie algebras over algebraically closed fieldsof characteristic O and over the field of real numbers. The models given are based on the algebras ofCayley numbers (octonions) and on exceptional Jordan algebras. They are also valid forcharacteristics p * 2. The book also provides an introduction to the problem of forms of exceptionalsimple Lie algebras, especially the exceptional D4 's, � 6 's, and � 7 's. These are studied by means ofconcrete realizations of the automorphism groups.Exceptional Lie Algebras is a useful tool for the mathematical public in general-especially thoseinterested in the classification of Lie algebras or groups-and for theoretical physicists.

Handbook of Algebra

Handbook of Algebra Book
Author : M. Hazewinkel
Publisher : Elsevier
Release : 2000-04-06
ISBN : 9780080532967
Language : En, Es, Fr & De

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Book Description :

Handbook of Algebra

Groups St Andrews 1997 in Bath

Groups St  Andrews 1997 in Bath Book
Author : C. M. Campbell,E. F. Robertson,G. C. Smith,N. Ruskuc
Publisher : Cambridge University Press
Release : 1999
ISBN : 9780521655767
Language : En, Es, Fr & De

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Book Description :

This two-volume book contains selected papers from the international conference "Groups St. Andrews 1997 in Bath". The articles are arranged in roughly alphabetical order and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles contributed by other conference participants. Proceedings of earlier "Groups St. Andrews" conferences have had a major impact on the development of group theory and these volumes should be equally important.

Hopf Algebras and Their Actions on Rings

Hopf Algebras and Their Actions on Rings Book
Author : Susan Montgomery
Publisher : American Mathematical Soc.
Release : 1993-10-28
ISBN : 0821807382
Language : En, Es, Fr & De

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Book Description :

The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.

Clifford Algebras and the Classical Groups

Clifford Algebras and the Classical Groups Book
Author : Ian R. Porteous,Porteous Ian R.
Publisher : Cambridge University Press
Release : 1995-10-05
ISBN : 9780521551779
Language : En, Es, Fr & De

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Book Description :

Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G[subscript 2], and the triality automorphism of Spin 8.

Structure of Factors and Automorphism Groups

Structure of Factors and Automorphism Groups Book
Author : Masamichi Takesaki
Publisher : American Mathematical Soc.
Release : 1983-12-31
ISBN : 9780821807019
Language : En, Es, Fr & De

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Book Description :

This book describes the recent development in the structure theory of von Neumann algebras and their automorphism groups. It can be viewed as a guided tour to the state of the art.

Structure of Factors and Automorphism Groups

Structure of Factors and Automorphism Groups Book
Author : Masamichi Takesaki
Publisher : American Mathematical Soc.
Release : 1983-12-31
ISBN : 9780821807019
Language : En, Es, Fr & De

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Book Description :

This book describes the recent development in the structure theory of von Neumann algebras and their automorphism groups. It can be viewed as a guided tour to the state of the art.