Cyclic homology /
This book is a comprehensive study of cyclic homology theory. The first partdeals with Hochschild and cyclic homology of associative algebras, their variations (periodic theory, dihedral theory) and the comparison with de Rham comology theory. The second part deals with cyclic sets, cyclic spaces, t...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
1992.
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| Series: | Grundlehren der mathematischen Wissenschaften ;
301. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book is a comprehensive study of cyclic homology theory. The first partdeals with Hochschild and cyclic homology of associative algebras, their variations (periodic theory, dihedral theory) and the comparison with de Rham comology theory. The second part deals with cyclic sets, cyclic spaces, their relationships with S 1-equivariant homology and the Chern character of Connes. The third part is devoted to the homology of the Lie algebra of matrices (the Loday-Quillen-Tsygan theorem) and its variations (namely non-commutative Lie homology). The fourth part is an account of algebraic K-theory and its relationship to cyclic homology. The last chapter is an overview of some applications tonon-commutative differential geometry (foliations, Novikov conjecture, idempotent conjecture) as devised by Alain Connes. Most of the results treated in this book have already appeared in research articles. However some are new (non-commutative Lie homology for instance) and many proofs are either more explicit or simpler than the existing ones. Though this book was thought of a basic reference for researchers, several part of it are accessible to graduate students, since the material is almost self contained. It also contains a comprehensive list of references on the subject. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xvi, 454 pages) : illustrations. |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 431-444) and index. |
| ISBN: | 9783662217399 (electronic bk.) 3662217392 (electronic bk.) |