Faithfully Flat Hopf Bi-Galois Extensions |
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| Authors: | Caihong Wang Shenglin Zhu |
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| Institution: | 1. School of Mathematics and Information Science , Henan Polytechnic University , Jiaozuo , China wwcaihong@yahoo.com.cn;3. School of Mathematical Sciences , Fudan University , Shanghai , China |
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| Abstract: | This article is devoted to faithfully flat Hopf bi-Galois extensions defined by Fischman, Montgomery, and Schneider. Let H be a Hopf algebra with bijective antipode. Given a faithfully flat right H-Galois extension A/R and a right H-comodule subalgebra C ? A such that A is faithfully flat over C, we provide necessary and sufficient conditions for the existence of a Hopf algebra W so that A/C is a left W-Galois extension and A a (W, H)-bicomodule algebra. As a consequence, we prove that if R = k, there is a Hopf algebra W such that A/C is a left W-Galois extension and A a (W, H)-bicomodule algebra if and only if C is an H-submodule of A with respect to the Miyashita–Ulbrich action. |
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| Keywords: | Hopf algebra Hopf bi-Galois extension Hopf–Galois object |
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