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Physics of Particles and Nuclei

, Volume 43, Issue 5, pp 663–665 | Cite as

On the variational noncommutative poisson geometry

  • A. V. Kiselev
Article

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.

Keywords

Jacobi Identity Leibniz Rule Evolutionary Vector Schouten Bracket Cyclic Invariance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • A. V. Kiselev

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