Secondary Hochschild homology and differentials

Abstract

In this paper we study a generalization of Kähler differentials, which correspond to the secondary Hochschild homology associated to a triple (A, B, ε). We establish computations in low dimension, while also showing how this connects with the kernel of a multiplication map.Definition 2.1. ([15]) We call (A, B, ε) a triple if A is a -algebra, B is a commutative -algebra, and ε : B −→ A is a morphism of -algebras such that ε(B) ⊆ Z(A). Call (A, B, ε) a commutative triple if A is also commutative.