The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures
High Energy Physics - Theory
2009-10-30 v2 dg-ga
Differential Geometry
Quantum Algebra
q-alg
Abstract
The super or Z_2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors \Lambda of even order. The corresponding super `Jacobi identities' are expressed by stating that these tensors have zero super Schouten-Nijenhuis bracket with themselves [\Lambda,\Lambda]=0. As a particular case, we provide the linear generalized super-Poisson structures which can be constructed on the dual spaces of simple superalgebras with a non-degenerate Killing metric. The su(3,1) superalgebra is given as a generic example.
Keywords
Cite
@article{arxiv.hep-th/9612186,
title = {The Z_2-graded Schouten-Nijenhuis bracket and generalized super-Poisson structures},
author = {J. A. de Azcarraga and J. M. Izquierdo and A. M. Perelomov and J. C. Perez Bueno},
journal= {arXiv preprint arXiv:hep-th/9612186},
year = {2009}
}
Comments
Latex/RevTeX file. 25 pages. Minor corrections and references added. To appear in J. Math. Phys