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Existence of critical modules of GK-dimension 2 over elliptic algebras
Author(s):
Kaushal
Ajitabh
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2843-2849.
MSC (2000):
Primary 16G50, 16P90, 16W50, 18G10
Posted:
April 7, 2000
MathSciNet review:
1664293
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Abstract:
We show that over an elliptic algebra, critical modules of Gelfand-Kirillov dimension 2 exist in all multiplicities (assuming the ground field is uncountable, algebraically closed). Geometrically, this shows that in a quantum plane there exist ``irreducible curve" modules of all possible degrees.
References:
- [Aj]
- K. Ajitabh, Modules over elliptic algebras and quantum planes, Proc. Lond. Math. Soc. (3)72 (1996), 567-587. MR 97a:16049
- [AjV]
- K. Ajitabh and M.Van den Bergh, Presentation of critical modules of GK-dimension 2 over elliptic algebras, Proc. American Math. Soc. 127, Number 6 (1999), 1633-1639. MR 99i:16046
- [ATV1]
- M. Artin, J. Tate, and M. Van den Bergh, Some algebras associated to automorphisms of elliptic curves, The Grothendieck Festschrift I, 33-85, Birkhäuser, Boston, 1990. MR 92e:14002
- [ATV2]
- M. Artin, J. Tate, and M. Van den Bergh, Modules over regular algebras of dimension 3, Invent. Math. 106 (1991), 335-388. MR 93e:16055
- [AV]
- M. Artin and M. Van den Bergh, Twisted homogeneous coordinate rings, J. Algebra 133 (1990), 249-271. MR 91k:14003
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Additional Information:
Kaushal
Ajitabh
Affiliation:
Department of Mathematics, Florida International University, University Park, Miami, Florida 33199
Email:
ajitabhk@solix.fiu.edu
DOI:
10.1090/S0002-9939-00-05322-3
PII:
S 0002-9939(00)05322-3
Keywords:
Elliptic algebras,
quantum planes,
regular algebras,
critical modules,
Cohen-Macaulay modules
Received by editor(s):
June 17, 1998
Received by editor(s) in revised form:
November 5, 1998
Posted:
April 7, 2000
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
2000,
American Mathematical Society
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