2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66250We show that the associative algebra structure can be incorporated in the BRST quantization formalism for gauge theories such that extension from the corresponding Lie algebra to the associative algebra is achieved using operator quantization of reducible gauge theories. The BRST differential that encodes the associativity of the algebra multiplication is constructed as a second-order quadratic differential operator on the bar resolution.amsart++, xy, sidecap, times. 34pp. V2: similar to (a slight expansion of) the version in Theoretical and Mathematical Physics 136 (2003) 1189--1211Quantum AlgebraHigh Energy Physics - TheoryMathematical Physicstext