Let F be an algebraically closed field of characteristic 0,H be an eight-dimensional non-semisimple Hopf algebra which is neither pointed nor unimodular and M2（F）be the full matrix algebra of 2×2 over F.In this...Let F be an algebraically closed field of characteristic 0,H be an eight-dimensional non-semisimple Hopf algebra which is neither pointed nor unimodular and M2（F）be the full matrix algebra of 2×2 over F.In this paper,we discuss and classify all H-module algebra structures on M2（F）.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(Grant Nos.1127104311471186)
文摘Let F be an algebraically closed field of characteristic 0,H be an eight-dimensional non-semisimple Hopf algebra which is neither pointed nor unimodular and M2（F）be the full matrix algebra of 2×2 over F.In this paper,we discuss and classify all H-module algebra structures on M2（F）.
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
