  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.
