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The excision theorems in Hochschild and cyclic homologies

Published online by Cambridge University Press:  20 March 2014

Guram Donadze  and
Manuel Ladra
Guram Donadze
Affiliation:
Kerala School of Mathematics, Kunnamangalam PO, Kozhikode-673 571, Kerala, India, (gdonad@gmail.com)
Manuel Ladra
Affiliation:
Department of Algebra, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain, (manuel.ladra@usc.es)
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 2 , April 2014 , pp. 305 - 317
Copyright
Copyright © Royal Society of Edinburgh 2014 

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