Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable...Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).展开更多
基金The NSF (19771046) of China and Anhui Province Education Committee Fund (99jl0209).
文摘Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).
