Jean-Louis Loday

Cyclic Homology (eBook, PDF)

• Format: PDF

Produktbeschreibung

In this 2nd edition a new chapter 13 on MacLane (co)homology is added. It is compared with a variant of algebraic K-theory called stable K-theory. It turns out that these two theories are isomorphic. The main tool for this comparison is a third theory constructed from derived functors over the category of polynomial functors. This chapter is a transition from the content of the first 12 ch.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 516
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9783662113899
• Artikelnr.: 53148919

Autorenporträt

In this 2nd edition a new chapter 13 on MacLane (co)homology is added. It is compared with a variant of algebraic K-theory called stable K-theory. It turns out that these two theories are isomorphic. The main tool for this comparison is a third theory constructed from derived functors over the category of polynomial functors. This chapter is a transition from the content of the first 12 ch.

Inhaltsangabe

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.

Rezensionen

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 (in the last chapter) 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 co