Almost Commutative Q-algebras and Derived brackets
Quantum Algebra
2020-09-02 v2 Mathematical Physics
math.MP
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\u{\i}ntrob'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.
Cite
@article{arxiv.1806.02662,
title = {Almost Commutative Q-algebras and Derived brackets},
author = {Andrew James Bruce},
journal= {arXiv preprint arXiv:1806.02662},
year = {2020}
}
Comments
15 pages. Accepted for publication in The Journal of Noncommutative Geometry