Cyclic Homology. Jean-Louis Loday. This book is a comprehensive study of cyclic homologytheory. The first partdeals with Hochschild and cyclichomology of associative algebras, their variations periodictheory, dihedral theory and the comparison with de Rhamcomology theory.
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Cyclic Homology. Jean-Louis Loday. This book is a comprehensive study of cyclic homologytheory. The first partdeals with Hochschild and cyclichomology of associative algebras, their variations periodictheory, dihedral theory and the comparison with de Rhamcomology theory. The third partis 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 anaccount of algebraic K-theory and its relationship to cyclichomology. The last chapter is an overview of someapplications tonon-commutative differential geometry foliations, Novikov conjecture, idempotent conjecture asdevised by Alain Connes. Most of the results treated in thisbook have already appeared in research articles.
Howeversome are new non-commutative Lie homology for instance andmany proofs are either more explicit or simpler than theexisting ones. Though this book was thought of a basicreference for researchers, several part of it are accessibleto graduate students, since the material is almost selfcontained.
It also contains a comprehensive list ofreferences on the subject. Classical Invariant Theory. Hochschild Homology.
It seems that you're in Germany. We have a dedicated site for Germany. 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.
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