Bar Simplicial Modules and Secondary Cyclic (Co)homology

Abstract

In this paper we study the simplicial structure of the complex $C^{\bullet }((A,B,\epsilon );M)$, associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object $\mathcal{B}(A,B,\epsilon )$, which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cyclic (co)homology and establish some of its properties (Theorems 3.9 and 4.11).

17 pages