Two-sided ideals in the ring of differential operators on a\n Stanley-Reisner ring

2014/07/07 by Ketil Tveiten, Tveiten, Ketil
Computer Science · Mathematics · #13F55 #13N10 #16S32 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.1643

openalex publication_date 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Stanley-Reisner ring (that is, a reduced monomial ring) with\ncoefficients in a domain k, and K its associated simplicial complex. Also let\nD_k(R) be the ring of k-linear differential operators on R. We give two\ndifferent descriptions of the two-sided ideal structure of D_k(R) as being in\nbijection with certain well-known subcomplexes of K; one based on explicit\ncomputation in the Weyl algebra, valid in any characteristic, and one valid in\ncharacteristic p based on the Frobenius splitting of R. A result of Traves\n[Tra99] on the D_k(R)-module structure of R is also given a new proof and\ndifferent interpretation using these techniques.\n

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