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
The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the ...The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.展开更多
基金the National Natural Science Foundation of China (No.10571153)the Educational Ministry Science Technique Research Key Foundation of China (No.108154)the Grant for Young Teachers of Nanjing Agricultural University (No.KJ06025)
文摘This paper mainly gives a Maschke-type theorem for two-sided weak smash products over semisimple weak Hopf algebras.
基金Supported by the Educational Ministry Science Technique Research Key Foundation of China (108154)the National Natural Science Foundation of China (10871170)
文摘This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.
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.
基金The Scientific Research Innovation Project for College Graduates in Jiangsu Province(No.CXLX_0094)
文摘The concept of weak Hopf group coalgebras is a natural generalization of the notions of both weak Hopf algebras（quantum groupoids） and Hopf group coalgebras.Let π be a group.The Morita context is considered in the sense of weak Hopf π-coalgebras.Let H be a finite type weak Hopf π-coalgebra,and A a weak right π-H-comodule algebra.It is constructed that a Morita context connects A#H＊ which is a weak smash product and the ring of coinvariants AcoH.This result is the generalization of that of Wang＇s in the paper ＂Morita contexts,π-Galois extensions for Hopf π-coalgebras＂ in 2006.Furthermore,the result is important for constructing weak π-Galois extensions.
