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), 14391451
MSC:
Primary 16S32; Secondary 14H20
DOI:
https://doi.org/10.1090/S00029947199512734802
MathSciNet review:
1273480
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Abstract  References  Similar Articles  Additional Information
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 finitedimensional 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 finitedimensional $k$algebra and $t \geqslant 1$ is any integer there exists such an $S$ with \[ H(S) \cong \left ( {\begin {array}{*{20}{c}} A & {\ast } \\ 0 & {{M_t}(k)} \\ \end {array} } \right ).\] 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 $\mathcal {D}(S)$.

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Additional Information
Keywords:
Differential operators,
finitedimensional algebras,
Morita equivalences,
diagonals,
subspace sytems,
curves,
singularities
Article copyright:
© Copyright 1995
American Mathematical Society