In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is ...In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.展开更多
In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is ...In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.展开更多
The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-H...The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-Hopf π-module in- troduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopf π-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.展开更多
R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the con...R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the展开更多
Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#...Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product展开更多
Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0&...Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion展开更多
基金Supported by the National Natural Science Foundation of China（10871170） Supported by the Educational Minister Science Technology Key Foundation of China（108154）
文摘这份报纸，主要由一种新方法为模块 coalgebras 给结构定理，并且删除 Hopf 代数学 H 的相对极 S 是 bijective 的条件。
文摘In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.
文摘In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras.
基金Project supported by the Program for New Century Excellent Talents in University (No. 04-0522), the National Science Foundation of Zhejiang Province of China (No. 102028), and the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 704004)
文摘The notion of weak Doi-Hopf π-datum and weak Doi-Hopf π-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in (B?hm, 2000), also as a generalization of a Doi-Hopf π-module in- troduced in (Wang, 2004). Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopf π-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.
文摘R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the
基金Project supported by the National Natural Science Foundation of China.
文摘Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product
文摘Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A<sub>0</sub>#<sub>σ</sub>H as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion
