Twisted Cyclic Homology And Crossed Product Algebras

Abstract

HC * (A ⋊ G) is the cyclic homology of the crossed product algebra A ⋊ G. For any gǫG we will define a homomorphism from HC g * (A), the twisted cylic homology of A with respect to g, to HC * (A ⋊ G). If G is the finite cyclic group generated by g and |G| = r is invertible in k, then HC * (A ⋊ G) will be isomorphic to a direct sum of r copies of HC g * (A). For the case where |G| is finite and Q ⊂ k we will generalize the Karoubi and Connes periodicity exact sequences for HC g * (A) to Karoubi and Connes periodicity exact sequences for HC * (A ⋊ G) .