On the Hochschild cohomology of a map between commutative differential graded algebras

Abstract

Abstract We consider a surjective morphism between commutative differential graded algebras ϕ: (∧V, d) → (B, d), where V is finite dimensional, and (B, d) is a module over ∧V via the mapping ϕ. We show that the Hochschild cohomology HH*(∧V; B) can be computed in terms of the graded vector space of positive ϕ-derivations. Moreover, if V is finite dimensional, then HH*(∧V; B) contains a polynomial algebra.