%0 Journal Article
%T Linear Odd Poisson Bracket on Grassmann Variables
%A V. A. Soroka
%J Physics
%D 1998
%I arXiv
%R 10.1016/S0370-2693(99)00228-2
%X 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 $\Delta$-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 $\Delta$-operator of the second order. It is shown that these $\Delta$-like operators together with a Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.
%U http://arxiv.org/abs/hep-th/9811252v3