扭曲Ehresmann Schauenburg双代数胚
Twisted Ehresmann Schauenburg bialgebroids
摘要：
在对应的霍普夫代数是余交换的，且对应于这个分裂的霍普夫伽罗瓦扩张的酉上圈的象属于余不变子代数的中心的条件下，我们在分裂的霍普夫伽罗瓦扩张的EhresmannSchauenburg双代数胚上构造了一个可逆的正规2上圈.证明了这类EhresmannSchauenburg双代数胚同构于EhresmannSchauenburg双代数胚的一个2-上圈扭，对应于一个无上圈的Hopf Galois扩张，其中余代数是余不变子代数与霍普夫代数的Smash积（即$\C(B/#_σH, H)\simeq \C(B\#H, H)^{\tildeσ}$）.我们还研究了理论的情况下，伽罗瓦对象的基础是平凡的，但不需要的霍普夫代数是余交换的。
英文摘要：
We construct an invertible normalised 2 cocycle on the Ehresmann Schauenburg bialgebroid of a cleft Hopf Galois extension under the condition that the corresponding Hopf algebra is cocommutative and the image of the unital cocycle corresponding to this cleft Hopf Galois extension belongs to the centre of the coinvariant subalgebra. Moreover, we show that any Ehresmann Schauenburg bialgebroid of this kind is isomorphic to a 2-cocycle twist of the Ehresmann Schauenburg bialgebroid corresponding to a Hopf Galois extension without cocycle, where comodule algebra is an ordinary smash product of the coinvariant subalgebra and the Hopf algebra (i.e. $\C(B/#_σH, H)\simeq \C(B\#H, H)^{\tildeσ}$). We also study the theory in the case of a Galois object where the base is trivial but without requiring the Hopf algebra to be cocommutative.
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