BFV-BRST ANALYSIS OF THE CLASSICAL AND QUANTUM Q-DEFORMATIONS OF THE SL(2) ALGEBRA

BFV-BRST charge for quantum algebras is not unique. Different construc tions of it in classical and quantum phase space for the universal env eloping algebra of the q-deformed sl(2) are discussed. In the quantum framework a positive definite scalar product is used to introduce a co -BFV-BRST charge to study the cohomology problem by means of the techn iques of the non-deformed case. Moreover, deformation of the phase spa ce without deforming the generators of sl(2) is considered. HBAR-q-def ormation of the phase space is shown to yield the Witten's second defo rmation for sl(2). To study the BFV-BRST cohomology problem when both the quantum phase space and the group are deformed, a two-parameter de formation of sl(2) is proposed, and its BFV-BRST charge is given.