JournalsjncgVol. 6, No. 4pp. 749–771

Cyclic homologies of crossed modules of algebras

  • Guram Donadze

    Tbilisi Centre for Mathematical Sciences, Georgia
  • Nick Inassaridze

    Tbilisi Centre for Mathematical Sciences, Georgia
  • Emzar Khmaladze

    Tbilisi Centre for Mathematical Sciences, Georgia
  • Manuel Ladra

    Universidad de Santiago de Compostela, Spain
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Abstract

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. 749–771

DOI 10.4171/JNCG/104