Representation theory and the Zel'manov approach
Author(s)
Bibliographic Information
Representation theory and the Zel'manov approach
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 167 . Non-associative normed algebras ; v. 2）
Cambridge University Press, 2018
- : hardback
Available at / 35 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||EMA||167200037149207
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Note
Includes bibliographical references (p. 664-714) and indexes
Description and Table of Contents
Description
This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav-Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.
Table of Contents
- Preface
- 5. Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav-Palmer type non-associative theorem
- 6. Representation theory for non-commutative JB*-algebras and alternative C*-algebras
- 7. Zel'manov approach
- 8. Selected topics in the theory of non-associative normed algebras
- Bibliography of Volume 1
- Additional bibliography to Volume 2
- Symbol index for Volume 1
- Subject index for Volume 1
- Symbol index for Volume 2
- Subject index for Volume 2.
by "Nielsen BookData"
