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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of critical modules of GK-dimension 2 over elliptic algebras


Author: Kaushal Ajitabh
Journal: Proc. Amer. Math. Soc. 128 (2000), 2843-2849
MSC (2000): Primary 16G50, 16P90, 16W50, 18G10
Published electronically: 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.


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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: http://dx.doi.org/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
Published electronically: April 7, 2000
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society