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Linear Odd Poisson Bracket on Grassmann Algebra

Vyacheslav A. Soroka
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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, $Δ$-operator and ghost number operator is indicated.

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Vyacheslav A. Soroka. 2000-02-10. Linear Odd Poisson Bracket on Grassmann Algebra. https://arxiv.org/abs/math-ph/0002031

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