The Hochschild and (cotriple) cyclic homologies of crossed modules of (not necessarily unital) associative algebras are investigated. Wodzicki’s excision theorem is extended for inclusion crossed modules in the category of crossed modules of algebras. The cyclic and cotriple cyclic homologies of crossed modules are compared in terms of a long exact homology sequence, generalising the relative cyclic homology exact sequence.
Cite this article
Guram Donadze, Nick Inassaridze, Emzar Khmaladze, Manuel Ladra, Cyclic homologies of crossed modules of algebras. J. Noncommut. Geom. 6 (2012), no. 4, pp. 749–771DOI 10.4171/JNCG/104