Cyclic Homologies of Crossed Modules of Algebras

2008/12/03 by Guram Donadze, Donadze, Guram, Nick Inassaridze +5
Mathematics · #17B40 #17B56 #18G10 #18G50 #18G60 #19D55 #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT #msc:17B40 #msc:17B56 #msc:18G10 #msc:18G50 #msc:18G60 #msc:19D55

paper · pdf · doi:10.48550/arxiv.0812.0767

arxiv created 2008/12/03 · arxiv updated 2009/12/01

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 long exact homology sequence, generalising the relative cyclic homology exact sequence.

Related

• Cyclic homology of crossed products
• Cyclic homology of Hopf Galois extensions and Hopf algebras
• Cyclic homology of braided Hopf crossed products
• Periodic cyclic homology of crossed products
• Hopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras