Representation theory and the Zel'manov approach
著者
書誌事項
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
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注記
Includes bibliographical references (p. 664-714) and indexes
内容説明・目次
内容説明
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.
目次
- 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.
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