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arXiv · hep-th/9811252

Linear Odd Poisson Bracket on Grassmann Variables

V. A. Soroka
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Abstract

A linear odd Poisson bracket (antibracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent $Δ$-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson bracket having the only Grassmann-odd nilpotent differential $Δ$-operator of the second order. It is shown that these $Δ$-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.

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V. A. Soroka. 1999-03-24. Linear Odd Poisson Bracket on Grassmann Variables. https://doi.org/10.1016/s0370-2693(99)00228-2

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