On the variational noncommutative Poisson geometry

Abstract

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.

Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 pages

References in corpus (2)

• Geometry of jet spaces and integrable systems
• Variational Lie algebroids and homological evolutionary vector fields

Cited by in corpus (4)

• The geometry of variations in Batalin-Vilkovisky formalism
• The calculus of multivectors on noncommutative jet spaces
• The Jacobi identity for graded-commutative variational Schouten bracket revisited
• On the geometry of the Batalin-Vilkovisky Laplacian