Hopf-Galois systems and Kashiwara algebras
نویسنده
چکیده
This article is made up with two parts. In the first part, using a recent result of Schauenburg, one generalizes to the case when objects are faithfully flat over the ground ring, the full equivalence between the notions of Hopf-Galois objects and Hopf-Galois systems. In this last description, one gives explicitly an inverse for a Hopf-Galois object T together with its generalized antipode. In the second part of the article, one shows that the Kashiwara algebras introduced by Kashiwara in his study of crystal bases form Hopf-Galois systems under the coaction of a quantized enveloping algebra of a KacMoody algebra. Their classical limits are examples of Sridharan algebras.
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