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

Authors:
R. C. Cannings and M. P. Holland

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1439-1451

MSC:
Primary 16S32; Secondary 14H20

DOI:
https://doi.org/10.1090/S0002-9947-1995-1273480-2

MathSciNet review:
1273480

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the coordinate ring of a smooth affine curve over an algebraically closed field of characteristic zero . For a subalgebra of with integral closure denote by the ring of differential operators on and by the finite-dimensional factor of by its unique minimal ideal. The theory of diagonal -subspace systems is introduced. This is used to show that if is a finite-dimensional -algebra and is any integer there exists such an with

**[Be]**S. Brenner,*Endomorphism algebras of vector spaces with distinguished sets of subspaces*, J. Algebra**6**(1967), 100-114.**[Br]**K.A. Brown,*The Artin algebras associated with differential operators on singular affine curves*, Math Z.**206**(1991), 423-442.**[CH]**R.C. Cannings and M.P. Holland,*Right ideals of rings of differential operators*, J. Algebra**167**(1994), 116-141.**[CH2]**-,*Differential operators and finite dimensional algebras*, J. Algebra (to appear).**[CHM]**R.C. Cannings, M.P. Holland, and G. Masson,*Gorenstein curve singularities and self-dual diagonal systems of vector spaces*, in preparation.**[GP]**I.M. Gelfand and V.A. Ponomarev,*Problems of linear algebra and classification of quadruples of subspaces in a finite dimensional vector space*, Colloq. Math. Soc. János Bolyai, vol. 5, North-Holland, Amsterdam, 1970.**[KR]**H. Kraft and C. Riedtmann,*Geometry of representations of quivers*, Representations of Algebras (P. Webb, ed.), London Math. Soc. Lecture Note Ser., vol. 116, Cambridge Univ. Press, Cambridge, 1986, pp. 109-146.**[SS]**S.P. Smith and J.T. Stafford,*Differential operators on an affine curve*, Proc. London Math. Soc. (3)**56**(1988), 229-259.

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
16S32,
14H20

Retrieve articles in all journals with MSC: 16S32, 14H20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1273480-2

Keywords:
Differential operators,
finite-dimensional algebras,
Morita equivalences,
diagonals,
subspace sytems,
curves,
singularities

Article copyright:
© Copyright 1995
American Mathematical Society