Almost Commutative Q-algebras and Derived brackets

Abstract

We introduce the notion of \emph{almost commutative Q-algebras} and demonstrate how the derived bracket formalism of Kosmann-Schwarzbach generalises to this setting. In particular, we construct `almost commutative Lie algebroids' following Va\uıntrob's Q-manifold understanding of classical Lie algebroids. We show that the basic tenets of the theory of Lie algebroids carry over verbatim to the almost commutative world.

15 pages. Accepted for publication in The Journal of Noncommutative Geometry