Differential operators on monomial curves.
type: Item
instance of: scholarly article
title: Differential operators on monomial curves.
zbMATH Open document ID: 1086.13507
DOI: 10.1016/S0021-8693(03)00144-3
author: Eivind Eriksen
published in: Journal of Algebra
publication date: 2003-07-29T00:00:00Z
review text: Let \(k\) be a fixed algebraically closed field of characteristic 0, and \(X\) an affine monomial curve defined over \(k\). Then, \(X = \text{Spec}(A)\), where \(A=k[\Gamma]\) is the semigroup algebra over \(k\) defined by a numerical semigroup \(\Gamma\subseteq {\mathbb N}_0\). The author gives an explicit description of the ring \(D={\roman D}(A)\) of \(k\)-linear differential operators on \(A\), the associated graded ring \(\text{GR}{\roman D}(A)\), and the module of derivations \(\text{Der}_k(A)\). He also classifies all graded \(D\)-modules which are finitely generated torsion-free \(A\)-modules of rank 1, considered as modules over the subring \(A\subseteq {\roman D}(A)\).
Mathematics Subject Classification ID: 13N10
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 13A02
zbMATH DE Number: 1955953
zbMATH Keywords: semigroup algebra
zbMATH Keywords: algebraic \(D\)-module
zbMATH Keywords: differential operator
zbMATH Keywords: monomial curve
reviewed by: E. V. Pankrat'ev
MaRDI profile type: Publication
cites work: Q4274969
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full work available at URL: s0021-8693(03)00144-3
OpenAlex ID: W2005607898
description: scientific article; zbMATH DE number 1955953