Presentation of critical modules of GK-dimension 2 over elliptic algebras
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- by K. Ajitabh and M. Van den Bergh PDF
- Proc. Amer. Math. Soc. 127 (1999), 1633-1639 Request permission
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.References
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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
- MR Author ID: 176980
- Email: vdbergh@luc.ac.be
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1633-1639
- MSC (1991): Primary 16D50, 16E10, 18G10
- DOI: https://doi.org/10.1090/S0002-9939-99-04717-6
- MathSciNet review: 1485455