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

 

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


Authors: K. Ajitabh and M. Van den Bergh
Journal: Proc. Amer. Math. Soc. 127 (1999), 1633-1639
MSC (1991): Primary 16D50, 16E10, 18G10
Published electronically: February 18, 1999
MathSciNet review: 1485455
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that critical modules of Gelfand-Kirillov dimension 2 and multiplicity $d$ over an elliptic algebra have (up to modules of lower GK-dimension and shifting) a presentation by $d\times d$-matrices of linear forms. In the language of non-commutative algebraic geometry this amounts to a generic description of ``curves'' of degree $d$ in a projective quantum plane.


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Additional Information

K. Ajitabh
Affiliation: Department of Mathematics, Florida International University, University Park, Miami, Florida 33199
Email: ajitabhk@zeus.fiu.edu

M. Van den Bergh
Affiliation: Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, 3590 Diepenbeek, Belgium
Email: vdbergh@luc.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04717-6
PII: S 0002-9939(99)04717-6
Keywords: Elliptic algebras, quantum planes, regular algebra, critical modules, Cohen-Macaulay modules
Received by editor(s): September 23, 1997
Published electronically: February 18, 1999
Additional Notes: The second author is a senior researcher at the FWO
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society