Degenerate Odd Poisson Bracket on Grassmann Variables

V. A. Soroka

doi:10.1134/1.855725

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arXiv · hep-th/9811223

Degenerate Odd Poisson Bracket on Grassmann Variables

V. A. Soroka

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Abstract

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is presented. It is revealed that this bracket has at once three nilpotent $Δ$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $Δ$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.

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V. A. Soroka. 1999-01-21. Degenerate Odd Poisson Bracket on Grassmann Variables. https://doi.org/10.1134/1.855725

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