Symmetry on rings of differential operators

2020/05/17 by Quinlan-Gallego, Eamon
#Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2005.08236

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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