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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Differential operators, $ n$-branch curve singularities and the $ n$-subspace problem

Authors: R. C. Cannings and M. P. Holland
Journal: Trans. Amer. Math. Soc. 347 (1995), 1439-1451
MSC: Primary 16S32; Secondary 14H20
MathSciNet review: 1273480
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Abstract: Let $ R$ be the coordinate ring of a smooth affine curve over an algebraically closed field of characteristic zero $ k$. For $ S$ a subalgebra of $ R$ with integral closure $ R$ denote by $ \mathcal{D}(S)$ the ring of differential operators on $ S$ and by $ H(S)$ the finite-dimensional factor of $ \mathcal{D}(S)$ by its unique minimal ideal. The theory of diagonal $ n$-subspace systems is introduced. This is used to show that if $ A$ is a finite-dimensional $ k$-algebra and $ t \geqslant 1$ is any integer there exists such an $ S$ with

$\displaystyle H(S) \cong \left( {\begin{array}{*{20}{c}} A & {\ast} \\ 0 & {{M_t}(k)} \\ \end{array} } \right).$

Further, the Morita classes of $ H(S)$ are classified for curves with few branches, and it is shown how to lift Morita equivalences from $ H(S)$ to $ \mathcal{D}(S)$.

References [Enhancements On Off] (What's this?)

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Keywords: Differential operators, finite-dimensional algebras, Morita equivalences, diagonals, subspace sytems, curves, singularities
Article copyright: © Copyright 1995 American Mathematical Society