Almost Commutative Q-algebras and Derived brackets
arXiv:1806.02662 · doi:10.4171/JNCG/377
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.
arXiv comment15 pages. Accepted for publication in The Journal of Noncommutative Geometry
References in corpus (11)
- The Geometry of the Master Equation and Topological Quantum Field Theory
- Higher derived brackets and homotopy algebras
- Derived brackets
- Some title containing the words "homotopy" and "symplectic", e.g. this one
- Graded bundles and homogeneity structures
- -manifolds and Higher Analogs of Lie Algebroids
- Letters to Alan Weinstein about Courant algebroids
- Lie brackets on affine bundles
- Deformations of Linear Lie Brackets
- Noncommutative supergeometry and duality
- Introduction to graded bundles