Cyclic modules with ∞-simplicial faces and the cyclic homology of A∞-algebras

Resumo

A chain bicomplex for A_∞-algebras, which generalizes the Tsygan chain bicomplex in the theory of cyclic homology of associative algebras, is constructed by using the techniques of differential modules with ∞-simplicial faces and D_∞-differential modules. For homotopy unital A_∞-algebras, an exact sequence generalizing the Connes–Tsygan exact sequence for unital associative algebras is obtained.