Produktinformationen zu „Cyclic Homology “
This book is a comprehensive study of cyclic homology theory. The first part deals 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 S1-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 to non-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 areeither 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.
Klappentext zu „Cyclic Homology “
From the reviews: "This is a very interesting book containing material for a comprehensive study of the cyclid homological theory of algebras, cyclic sets and S1-spaces. Lie algebras and algebraic K-theory and an introduction to Connes'work and recent results on the Novikov conjecture. The book requires a knowledge of homological algebra and Lie algebra theory as well as basic technics coming from algebraic topology. The bibliographic comments at the end of each chapter offer good suggestions for further reading and research. The book can be strongly recommended to anybody interested in noncommutative geometry, contemporary algebraic topology and related topics." European Mathematical Society Newsletter
Inhaltsverzeichnis zu „Cyclic Homology “
1. Hochschild Homology.- 2. Cyclic Homology of Algebras.- 3. Smooth Algebras and Other Examples.- 4. Operations on Hochschild and Cyclic Homology.- 5. Variations on Cyclic Homology.- 6. The Cyclic Category, Tor and Ext Interpretation.- 7. Cyclic Spaces and Sl-Equivariant Homology.- 8. Chern Character.- 9. Classical Invariant Theory.- 10. Homology of Lie Algebras of Matrices.- 11. Algebraic K-Theory.- 12. Non-commutative Differential Geometry.- 13. Mac Lane (co)homology.- Appendices.- A. Hopf Algebras.- B. Simplicial.- C. Homology of Discrete Groups and Small Categories.- D. Spectral Sequences.- E. Smooth Algebras.- References.- References 1992-1996.- Symbols.
Bibliographische Angaben
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Autor:
Jean-Louis Loday
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1997, 2nd ed., 516 Seiten, 24 Abbildungen, Maße: 16,1 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540630740
- ISBN-13: 9783540630746
- Erscheinungsdatum: 12.11.1997
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