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arXiv · 2005.08236

Symmetry on rings of differential operators

Eamon Quinlan-Gallego
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Abstract

If $k$ is a field and $R$ is a commutative $k$-algebra, we explore the question of when the ring $D_{R|k}$ of $k$-linear differential operators on $R$ is isomorphic to its opposite ring. Under mild hypotheses, we prove this is the case whenever $R$ Gorenstein local or when $R$ is a ring of invariants. As a key step in the proof we show that in many cases of interest canonical modules admit right $D$-module structures. After this work was completed we realized that some of our results were already proved in higher generality by Yekutieli, albeit using more sophisticated methods.

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Eamon Quinlan-Gallego. 2020-05-17. Symmetry on rings of differential operators. https://arxiv.org/abs/2005.08236

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