论文标题
差分运算符环上的对称性
Symmetry on rings of differential operators
论文作者
论文摘要
如果$ k $是一个字段，而$ r $是交换性$ k $ -algebra，我们将探讨$ r $上的$ k $ linear差速器运算符$ d_ {r | k} $何时与其相对的戒指同构。在温和的假设下，每当$ r $ gorenstein local或$ r $是不变的戒指时，我们就会证明情况。作为证明的关键步骤，我们表明，在许多感兴趣的情况下，规范模块承认正确的$ d $模块结构。 完成这项工作后，我们意识到，Yekutieli已经证明了我们的一些结果，尽管使用了更复杂的方法。
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.
