It is shown that the BRST charge Q for any gauge model with a Lie algebra
symmetry may be decomposed as Q=\del+\del^{\dag}, \del^2=\del^{\dag 2}=0,
[\del, \del^{\dag}]_+=0 provided dynamical Lagrange multipliers are used but
without introducing other matter variables in \del than the gauge generators
in Q. Furthermore, \del is shown to have the form \del=c^{\dag a}\phi_a
(or ϕa′​c†a) where ca are anticommuting expressions in the
ghosts and Lagrange multipliers, and where the non-hermitian operators ϕa​
satisfy the same Lie algebra as the original gauge generators. By means of a
bigrading the BRST condition reduces to \del|ph\hb=\del^{\dag}|ph\hb=0 which
is naturally solved by c^a|ph\hb=\phi_a|ph\hb=0 (or c^{\dag
a}|ph\hb={\phi'_a}^{\dag}|ph\hb=0). The general solutions are shown to have a
very simple form.Comment: 18 pages, Late