On a different BRST constructions for a given Lie algebra

The method of the BRST quantization is considered for the system of constraints, which form a Lie algebra. When some of the Cartan generators do not imply any conditions on the physical states, the system contains the first and the second class constraints. After the introduction auxiliary bosonic degrees of freedom for these cases, the corresponding BRST charges with the nontrivial structure of nonlinear terms in ghosts are constructed.