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.
Cite
@article{arxiv.1112.5784,
title = {On the variational noncommutative Poisson geometry},
author = {Arthemy V. Kiselev},
journal= {arXiv preprint arXiv:1112.5784},
year = {2012}
}
Comments
Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 pages