Frobenius和拟Frobenius左Hopf代数群

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2025-01-01 DOI:10.1016/j.jpaa.2024.107844

Sophie Chemla

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引用次数: 0

摘要

我们研究了Takeuchi-Schauenburg意义上的左（op）Hopf代数群何时产生Frobenius或拟Frobenius扩展。对于Hopf代数群在Böhm意义上的情况，用G. Böhm（[4]）处理。与Hopf代数群相反，（op）Hopf左代数群不一定有对映体，但它们的Hopf-伽罗瓦映射是可逆的。利用了关于左Hopf代数群（[18],[35],[25]）的最新结果。我们的结果应用于一类受限Lie-Rinehart代数的受限包络代数。

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Frobenius and quasi-Frobenius left Hopf algebroids

We study when left (op)Hopf algebroids in the sense of Takeuchi-Schauenburg give rise to a Frobenius or quasi-Frobenius extension. The case of Hopf algebroids in the sense of Böhm was treated by G. Böhm ([4]). Contrary to Hopf algebroids, (op)Hopf left algebroids don't necessarily have an antipode but their Hopf-Galois map is invertible. We make use of recent results about left Hopf algebroids ([18], [35], [25]). Our results are applied to the restricted enveloping algebra of a restricted Lie-Rinehart algebra.

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.