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Linear Odd Poisson Bracket on Grassmann Algebra

Mathematical Physics 2007-05-23 v1 High Energy Physics - Theory Group Theory math.MP

Abstract

A linear odd Poisson bracket realized solely in terms of Grassmann variables is suggested. It is revealed that with the bracket, corresponding to a semi-simple Lie group, both a Grassmann-odd Casimir function and invariant (with respect to this group) nilpotent differential operators of the first, second and third orders are naturally related and enter into a finite-dimensional Lie superalgebra. A connection of the quantities, forming this Lie superalgebra, with the BRST charge, Δ\Delta-operator and ghost number operator is indicated.

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Cite

@article{arxiv.math-ph/0002031,
  title  = {Linear Odd Poisson Bracket on Grassmann Algebra},
  author = {Vyacheslav A. Soroka},
  journal= {arXiv preprint arXiv:math-ph/0002031},
  year   = {2007}
}

Comments

8 pages, LATEX 2.09. The talk given at the International Seminar "Supersymmetries and Quantum Symmetries" (SQS'99, JINR, Dubna, Russia, 27-31 July, 1999). To be published in the Proceedings of this Seminar