$\mathcal{D}$ -modules with finite support are semi-simple

Rolf Källström Department of Mathematics, University of Gävle

Rings and Algebras mathscidoc:1701.31004

Arkiv for Matematik, 52, (2), 291-299, 2012.8
Let $(R, \frak{m}, k_{R})$ be a regular local$k$-algebra satisfying the weak Jacobian criterion, and such that$k$_{$R$}/$k$is an algebraic field extension. Let $\mathcal{D}_{R}$ be the ring of$k$-linear differential operators of$R$. We give an explicit decomposition of the $\mathcal{D}_{R}$ -module $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}_{R}^{n+1}$ as a direct sum of simple modules, all isomorphic to $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}$ , where certain “Pochhammer” differential operators are used to describe generators of the simple components.
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  title={ $\mathcal{D}$ -modules with finite support are semi-simple},
  author={Rolf Källström},
  booktitle={Arkiv for Matematik},
Rolf Källström. $\mathcal{D}$ -modules with finite support are semi-simple. 2012. Vol. 52. In Arkiv for Matematik. pp.291-299. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203638128469065.
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