Linear Odd Poisson Bracket on Grassmann Algebra

Details Linear Odd Poisson Bracket on Grassmann Algebra Linear Odd Poisson Bracket on Grassmann Algebra

2000-02-10

arxiv.org/abs/math-ph/0002031v1

Physics

Mathematical Physics

8 pages, LATEX 2.09. The talk given at the International Seminar "Supersymmetries and Quantum Symmetries" (SQS'99, JINR, Dubna

Scientific paper

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, $\Delta$-operator and ghost number operator is indicated.

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