Classification of Ring and $C^\ast $-Algebra Direct Limits of Finite-Dimensional Semisimple Real Algebras PDF Download

Author: K. R. Goodearl
Publisher: American Mathematical Soc.
ISBN: 082182435X
Category : Mathematics
Languages : en
Pages : 161

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Book Description
Motivated by (i) Elliott's classification of direct limits of countable sequences of finite-dimensional semisimple complex algebras and complex AF C*-algebras, (ii) classical results classifying involutions on finite-dimensional semisimple complex algebras, and (iii) the classification by Handelman and Rossmann of automorphisms of period two on the algebras appearing in (i) we study the real algebras described above and completely classify them, up to isomorphism, Morita equivalence, or stable isomorphism. We also show how our classification easily distinguishes various types of algebras within the given classes, and we partially solve the problem of determining exactly which values are attained by the invariants used in classifying these algebras.

Author: K.R. Goodearl
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Hoan Duong
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 200

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Book Description
The conjecture of (GH) concerning a proposed complete invariant for direct limit algebras is simplified, and we show that this invariant (essentially a diagram of ordered $K\sb0$-groups) is complete, establishing the conjecture.

Author: V. Dlab
Publisher: Springer Science & Business Media
ISBN: 9401715564
Category : Mathematics
Languages : en
Pages : 392

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Book Description
Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 1402051417
Category : Mathematics
Languages : en
Pages : 405

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Book Description
This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.

Author: Michiel Hazewinkel
Publisher: CRC Press
ISBN: 1351869868
Category : Mathematics
Languages : en
Pages : 285

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Book Description
The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Author: Yurij A. Drozd
Publisher: Berlin : Springer-Verlag
ISBN:
Category : Mathematics
Languages : en
Pages : 272

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Book Description
The theory of finite dimensional algebras is one of the most fundamental domains of modern algebra, applied in several other parts of mathematics and in theoretical physics. The only prior knowledge assumed of the reader is linear algebra and, in places, a little group theory.

Author: Ambar N. Sengupta
Publisher: Springer Science & Business Media
ISBN: 1461412315
Category : Mathematics
Languages : en
Pages : 383

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Book Description
This graduate textbook presents the basics of representation theory for finite groups from the point of view of semisimple algebras and modules over them. The presentation interweaves insights from specific examples with development of general and powerful tools based on the notion of semisimplicity. The elegant ideas of commutant duality are introduced, along with an introduction to representations of unitary groups. The text progresses systematically and the presentation is friendly and inviting. Central concepts are revisited and explored from multiple viewpoints. Exercises at the end of the chapter help reinforce the material. Representing Finite Groups: A Semisimple Introduction would serve as a textbook for graduate and some advanced undergraduate courses in mathematics. Prerequisites include acquaintance with elementary group theory and some familiarity with rings and modules. A final chapter presents a self-contained account of notions and results in algebra that are used. Researchers in mathematics and mathematical physics will also find this book useful. A separate solutions manual is available for instructors.

Author: G. A. Elliott
Publisher:
ISBN:
Category :
Languages : en
Pages : 21

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Book Description

Author: Michiel Hazewinkel
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 422

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Book Description
This second volume of this text covers the classical aspects of the theory of groups and their representations. It also offers a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. It reviews key recent developments in the theory of special ring classes including Frobenius, quasi-Frobenius, and others.