Almost commutative $Q$-algebras and derived brackets
Copyright policy )Almost commutative $Q$-algebras and derived brackets
We introduce the notion of 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 Vaıntrob’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.
- University of Luxembourg Luxembourg
almost commutative Lie algebroids, Almost commuative algebras, Supermanifolds and graded manifolds, Noncommutative geometry, FOS: Physical sciences, Lie algebroids, Mathematical Physics (math-ph), 81R60, 46L87, 17B75, Poisson manifolds; Poisson groupoids and algebroids, almost commutative algebras, Mathematics - Quantum Algebra, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Noncommutative geometry in quantum theory, Color Lie (super)algebras, almost commutative non-negatively graded algebra, Quantum Algebra (math.QA), : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Noncommutative differential geometry, homological \(p\)-derivations, Mathematical Physics
almost commutative Lie algebroids, Almost commuative algebras, Supermanifolds and graded manifolds, Noncommutative geometry, FOS: Physical sciences, Lie algebroids, Mathematical Physics (math-ph), 81R60, 46L87, 17B75, Poisson manifolds; Poisson groupoids and algebroids, almost commutative algebras, Mathematics - Quantum Algebra, FOS: Mathematics, : Mathematics [G03] [Physical, chemical, mathematical & earth Sciences], Noncommutative geometry in quantum theory, Color Lie (super)algebras, almost commutative non-negatively graded algebra, Quantum Algebra (math.QA), : Mathématiques [G03] [Physique, chimie, mathématiques & sciences de la terre], Noncommutative differential geometry, homological \(p\)-derivations, Mathematical Physics
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