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.

中文翻译：

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微分算子环上的对称性

如果k是一个域，而R是一个交换k -代数，我们将探讨当环$D_{\mathrm{电阻}|克}$R上的k 个线性微分算子与其相反的环同构。在温和的假设下，我们证明当R Gorenstein 局部或当R是不变量环时就是这种情况。作为证明的关键步骤，我们表明在许多感兴趣的情况下，规范模块承认正确的D模块结构。