Linear Odd Poisson Bracket on Grassmann Variables
Soroka, V. A.
arXiv, 9811252 / Harvested from arXiv
Text on arXiv
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.
Publié le : 1998-11-30
Classification:  High Energy Physics - Theory,  Mathematical Physics,  Mathematics - Group Theory 
@article{9811252,
     author = {Soroka, V. A.},
     title = {Linear Odd Poisson Bracket on Grassmann Variables},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9811252}
}

Soroka, V. A. Linear Odd Poisson Bracket on Grassmann Variables. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9811252/