Smooth Algebras and Other Examples
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This chapter is devoted to the computation of Hochschild and cyclic homologies of some particular types of algebras: tensor algebras, symmetric algebras, universal enveloping algebras of Lie algebras and, finally, smooth algebras, on which we put some emphasis. One more important example, the case of group algebras, will be treated later, in Sect. 7.4. It is also shown in this chapter that Hochschild and cyclic homology are related to many other theories such as the homology of Lie algebras, André-Quillen homology of commutative algebras, and Deligne cohomology.
KeywordsExact Sequence Spectral Sequence Commutative Algebra Polynomial Algebra Free Resolution
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Bibliographical Comments on Chapter 3
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- M. André, Homologie des algèbres commutatives, Springer Verlag, 1974.Google Scholar