Secondary Hochschild cohomology and derivations

Abstract

In this paper, we introduce a generalization of derivations. Using these socalled secondary derivations, along with an analogue of Connes' Long Exact Sequence, we are able to provide computations in low dimension for the secondary Hochschild and cyclic cohomologies associated to a commutative triple. We then establish a universal property, which paves the way to relating secondary Kähler differentials with the aforementioned secondary derivations.