2000/02/10 by Vyacheslav Soroka, Vyacheslav A. Soroka, Soroka, Vyacheslav A.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th #math-ph #math.GR #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0002031
8 pages, LATEX 2.09. The talk given at the International Seminar "Supersymmetries and Quantum Symmetries" (SQS'99, JINR, Dubna, Russia, 27-31 July, 1999). To be published in the Proceedings of this Seminar
arxiv created 2000/02/10 · arxiv updated 2009/11/30
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.