In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is g...In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopfalgebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.展开更多
基金Project supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004), the Program for New Century Excellent Talents in Univer-sity (No. 04-0522), and the Natural Science Foundation of Zhejiang Province (No. 102028), China
文摘In Artin algebra representation theory there is an important result which states that when the order of G is invertible in A then gl.dim（AG）=gl.dim（A）. With the development of Hopf algebra theory, this result is generalized to smash product algebra. As known, weak Hopfalgebra is an important generalization of Hopf algebra. In this paper we give the more general result, that is the relation of homological dimension between an algebra A and weak smash product algebra A#H, where H is a finite dimensional weak Hopf algebra over a field k and A is an H-module algebra.
