HOMOLOGICAL DIMENSION OF SMASH PRODUCT OVER QUASITRIANGULAR WEAK HOPF ALGEBRA

Abstract

Let (H, R) be a quasitriangular weak Hopf algebra, and A a quantum commutative weak H-module algebra. We establish the relationship of homological dimensions between weak smash product algebra A#H and A under some conditions. As an application, we consider the case of twisted weak Hopf algebra.