Degenerate Odd Poisson Bracket on Grassmann Variables

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 $\Delta$-like differential operators of the first, the second and the third orders with respect to the Grassmann derivatives. It is shown that these $\Delta$-like operators together with the Grassmann-odd nilpotent Casimir function of this bracket form a finite-dimensional Lie superalgebra.

5 pages, LATEX. Corrections of misprints. The relation (23) is added

References in corpus (1)

• A Lie Group Structure Underlying the Triplectic Geometry

Cited by in corpus (7)

• Nuclear structure corrections in the energy spectra of electronic and muonic deuterium
• Linear Odd Poisson Bracket on Grassmann Variables
• Odd Nambu bracket on Grassmann algebra
• Nucleus polarizability contribution to the hydrogen-deuterium isotope shift
• Nambu-like odd brackets on supermanifolds
• N=2 Supercomplexification of the Korteweg-de Vries, Sawada-Kotera and Kaup-Kupershmidt Equations
• Linear Odd Poisson Bracket on Grassmann Algebra