Article
Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations
Author/s | Narváez Macarro, Luis |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2020-01 |
Deposit Date | 2022-11-09 |
Published in |
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Abstract | Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the ... Let k be a commutative ring and A a commutative k-algebra. In this paper we introduce the notion of enveloping algebra of Hasse–Schmidt derivations of A over k and we prove that, under suitable smoothness hypotheses, the canonical map from the above enveloping algebra to the ring of differential operators DA/k is an isomorphism. This result generalizes the characteristic 0 case in which the ring DA/k appears as the enveloping algebra of the Lie-Rinehart algebra of the usual k-derivations of A provided that A is smooth over k. |
Citation | Narváez Macarro, L. (2020). Rings of differential operators as enveloping algebras of Hasse–Schmidt derivations. Journal of Pure and Applied Algebra, 224 (1), 320-361. https://doi.org/10.1016/j.jpaa.2019.05.009. |
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