The excision theorems in Hochschild and cyclic homologies

We study the excision property for Hochschild and cyclic homologies in the category of simplicial algebras. We extend Wodzicki's notion of H-unital algebras to simplicial algebras and then show that a simplicial algebra I* satisfies excision in Hochschild and cyclic homologies if and only if it...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2014-04, Vol.144 (2), p.305-317
Main Authors: Donadze, Guram, Ladra, Manuel
Format: Article
Language:English
Subjects:
Algebra
Categories
Homology
Mathematical analysis
Modules
Theorems
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Summary:We study the excision property for Hochschild and cyclic homologies in the category of simplicial algebras. We extend Wodzicki's notion of H-unital algebras to simplicial algebras and then show that a simplicial algebra I* satisfies excision in Hochschild and cyclic homologies if and only if it is H-unital. We use this result in the category of crossed modules of algebras and provide an answer to the question posed in the recent paper by Donadze et al. We also give (based on work by Guccione and Guccione) the excision theorem in Hochschild homology with coefficients.
ISSN:0308-2105
1473-7124
DOI:10.1017/S0308210512001874