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Bar Simplicial Modules and Secondary Cyclic (Co)homology (1605.03273v1)
Published 11 May 2016 in math.RA
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 3.9 and 4.11).