Bar simplicial modules and secondary cyclic (co)homology

Abstract

In this paper we study the simplicial structure of the complex C^{\bullet}((A,B,\varepsilon); M) , associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object \mathcal{B}(A,B,\varepsilon) , 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 4.11 and 5.11).