Differential operators, branch curve singularities and the subspace problem
Authors:
R. C. Cannings and M. P. Holland
Journal:
Trans. Amer. Math. Soc. 347 (1995), 14391451
MSC:
Primary 16S32; Secondary 14H20
MathSciNet review:
1273480
Fulltext 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 finitedimensional factor of by its unique minimal ideal. The theory of diagonal subspace systems is introduced. This is used to show that if is a finitedimensional algebra and is any integer there exists such an with Further, the Morita classes of are classified for curves with few branches, and it is shown how to lift Morita equivalences from to .
 [Be]
S. Brenner, Endomorphism algebras of vector spaces with distinguished sets of subspaces, J. Algebra 6 (1967), 100114.
 [Br]
K.A. Brown, The Artin algebras associated with differential operators on singular affine curves, Math Z. 206 (1991), 423442.
 [CH]
R.C. Cannings and M.P. Holland, Right ideals of rings of differential operators, J. Algebra 167 (1994), 116141.
 [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 selfdual 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, NorthHolland, 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. 109146.
 [SS]
S.P. Smith and J.T. Stafford, Differential operators on an affine curve, Proc. London Math. Soc. (3) 56 (1988), 229259.
 [Be]
 S. Brenner, Endomorphism algebras of vector spaces with distinguished sets of subspaces, J. Algebra 6 (1967), 100114.
 [Br]
 K.A. Brown, The Artin algebras associated with differential operators on singular affine curves, Math Z. 206 (1991), 423442.
 [CH]
 R.C. Cannings and M.P. Holland, Right ideals of rings of differential operators, J. Algebra 167 (1994), 116141.
 [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 selfdual 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, NorthHolland, 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. 109146.
 [SS]
 S.P. Smith and J.T. Stafford, Differential operators on an affine curve, Proc. London Math. Soc. (3) 56 (1988), 229259.
Similar Articles
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:
http://dx.doi.org/10.1090/S00029947199512734802
PII:
S 00029947(1995)12734802
Keywords:
Differential operators,
finitedimensional algebras,
Morita equivalences,
diagonals,
subspace sytems,
curves,
singularities
Article copyright:
© Copyright 1995
American Mathematical Society
