In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The...In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The authors prove that, if An is a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants AB = {a ∈ A ｜ b · a = ε（b）a, Ab ε B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AH as in the classical case. The results are applied to the case H = （kG）＊ for a finite group G to get a Galois 1-1 correspondence.展开更多
Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. U...Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.展开更多
基金supported by the National Natural Science Foundation of China(No.11331006)
文摘In this paper, the classical Galois theory to the H＊-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra, and A/An a right H＊-Galois extension. The authors prove that, if An is a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants AB = {a ∈ A ｜ b · a = ε（b）a, Ab ε B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AH as in the classical case. The results are applied to the case H = （kG）＊ for a finite group G to get a Galois 1-1 correspondence.
文摘Recently, we introduced the notion of a generalized derivation from a bimodule to a bimodule. In this paper, we give a more general notion based on commutators which covers generalized derivations as a special case. Using it, we show that the separability of an algebra extension is characterized by generalized derivations.
