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Symmetry on rings of differential operators
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-07-21 , DOI: 10.1016/j.jalgebra.2021.07.007 Eamon Quinlan-Gallego
中文翻译:
微分算子环上的对称性
更新日期:2021-07-30
Journal of Algebra ( IF 0.8 ) Pub Date : 2021-07-21 , DOI: 10.1016/j.jalgebra.2021.07.007 Eamon Quinlan-Gallego
If k is a field and R is a commutative k-algebra, we explore the question of when the ring 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:
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。