Differential operators, retracts, and toric face rings

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-10-03 DOI:10.2140/ant.2023.17.1959

Christine Berkesch, C-Y. Jean Chan, Patricia Klein, Laura Felicia Matusevich, Janet Page, Janet Vassilev

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引用次数: 2

Abstract

We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$ . For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators are induced by differential operators on the ambient ring. Lastly, we provide a criterion for the Gorenstein property of a normal affine semigroup ring in terms of its differential operators.

Our main technique is to realize the k-algebras we study in terms of a suitable family of their algebra retracts in a way that is compatible with the characterization of differential operators. This strategy allows us to describe differential operators of any k-algebra realized by retracts in terms of the differential operators on these retracts, without restriction on $char (k)$ .

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差速器操纵器、伸缩器和复曲面环

给出了特征为0的复曲面环的微分算子环的显式描述。对于正则仿射半群环的商，我们还确定了它们的微分算子中的哪一个是由环上的微分算子诱导的。最后，我们用微分算子给出了正规仿射半群环的Gorenstein性质的一个判据。我们的主要技术是以一种与微分算子的表征兼容的方式，实现我们根据其代数伸缩的合适族来研究的k-代数。该策略使我们能够根据伸缩器上的微分算子来描述由伸缩器实现的任何k-代数的微分算子，而不受字符的限制⁡ （k）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.