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Differential
operators, retracts, and toric face rings
Christine Berkesch, C-Y. Jean Chan, Patricia Klein, Laura Felicia Matusevich, Janet Page and Janet Vassilev |
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Vol. 17 (2023), No. 11, 1959–1984
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Abstract |
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We give explicit descriptions of rings of differential operators of toric face rings in characteristic . 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 . |
Keywords
differential operators, toric face rings, algebra retracts,
affine semigroup rings
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Mathematical Subject Classification
Primary: 16S32
Secondary: 13F55, 13N05
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Milestones
Received: 31 January 2022
Revised: 18 January 2023
Accepted: 23 February 2023
Published: 3 October 2023
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Authors |
| Christine Berkesch | |
| School of Mathematics University of Minnesota Minneapolis MN United States |
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| C-Y. Jean Chan | |
| Department of Mathematics Central Michigan University Mount Pleasant MI United States |
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| Patricia Klein | |
| Department of Mathematics Texas A&M University College Station TX United States |
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| Laura Felicia Matusevich | |
| Department of Mathematics Texas A&M University College Station TX United States |
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| Janet Page | |
| Mathematics Department North Dakota State University Fargo ND United States |
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| Janet Vassilev | |
| Department of Mathematics and
Statistics University of New Mexico Albuquerque NM United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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