BFV-BRST analysis of the classical and quantum q-deformations of the sl(2) algebra

BFV-BRST charge for q-deformed algebras is not unique. Different constructions of it in the classical as well as in the quantum phase space for the q-deformed algebra slq(2) are discussed. Moreover, deformation of the phase space without deforming the generators of sl(2) is considered. h -q-deformation of the phase space is shown to yield the Witten's second deformation. To study the BFV-BRST cohomology problem when both the quantum phase space and the group are deformed, a two parameter deformation of sl(2) is proposed, and its BFV-BRST charge is given. (author). 21 refs