Hopf–Galois Systems and Kashiwara Algebras
Hopf–Galois Systems and Kashiwara Algebras
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DOI：
10.1081/agb-120038639
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
C. Grunspan
中科院分区：
文献类型：
--
作者：
C. Grunspan
摘要本文由两部分组成。在第一部分中，使用绍恩堡最近的结果，人们将其推广到物体忠实地平坦在地环上的情况，即霍普夫-伽罗瓦物体和霍普夫-伽罗瓦系统的概念之间的完全等价。在最后的描述中，我们明确给出了 Hopf-Galois 对象 T 的逆及其广义对映体。文章的第二部分表明，柏原在晶体基研究中引入的柏原代数在 Kac-Moody 代数的量子化包络代数的共同作用下形成了 Hopf-Galois 系统。它们的经典极限是 Sridharan 代数的例子。
Abstract 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 Kac–Moody algebra. Their classical limits are examples of Sridharan algebras.