2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56503A 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.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 SeminarMathematical PhysicsHigh Energy Physics - TheoryGroup Theorytext