(A,δ)-modules, Hochschild homology and higher derivations.

In this paper, we develop the theory of modules over (A , δ) , where A is an algebra and δ : A ⟶ A is a derivation. Our approach is heavily influenced by Lie derivative operators in noncommutative geometry, which make the Hochschild homologies H H ∙ (A) of A into a module over (A , δ) . We also consider modules over (A , Δ) , where Δ = { Δ n } n ≥ 0 is a higher derivation on A. Further, we obtain a Cartan homotopy formula for an arbitrary higher derivation on A. [ABSTRACT FROM AUTHOR]