Homogenized
Authors:
Lieven Le Bruyn and S. P. Smith
Journal:
Proc. Amer. Math. Soc. 118 (1993), 725730
MSC:
Primary 16W50; Secondary 17B37
MathSciNet review:
1136235
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Abstract: This note studies a special case of Artin's projective geometry (Geometry of quantum planes, MIT, preprint, 1990) for noncommutative graded algebras. It is shown that (most of) the line modules over the homogenization of the enveloping algebra are in bijection with the lines lying on the quadrics that are the (closures of the) conjugacy classes in . Furthermore, these line modules are the homogenization of the Verma modules for .
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S. P. Smith and J. Staniszkis, Representations of the four dimensional Sklyanin algebra at points of infinite order, J. Algebra (to appear).
 [1]
 M. Artin, Geometry of quantum planes, preprint, MIT, 1990. MR 1144023 (93b:14004)
 [2]
 M. Artin, J. Tate, and M. Van den Bergh, Some algebras associated to automorphisms of elliptic curves, The Grothendieck Festschrift, Vol. I, Birkhäuser, Basel and Boston, 1990, pp. 3385. MR 1086882 (92e:14002)
 [3]
 V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327402. MR 833194 (87j:32030)
 [4]
 R. Hartshorne, Algebraic geometry, SpringerVerlag, 1977. MR 0463157 (57:3116)
 [5]
 T. Levasseur, Some properties of noncommutative regular graded rings, Glasgow Math. J. (to appear). MR 1181768 (93k:16045)
 [6]
 T. Levasseur and S. P. Smith, Modules over the dimensional Sklyanin algebra, preprint, Seattle, 1991.
 [7]
 Li Huishi and F. Van Oystaeyen, Dehomogenization of gradings to Zariskian filtrations and applications to invertible ideals, Proc. Amer. Math. Soc. (to appear). MR 1081698 (92h:16039)
 [8]
 S. P. Smith and J. T. Stafford, Regularity of the four dimensional Sklyanin algebra, Compositio Math, (to appear). MR 1175941 (93h:16037)
 [9]
 S. P. Smith and J. Staniszkis, Representations of the four dimensional Sklyanin algebra at points of infinite order, J. Algebra (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311362359
PII:
S 00029939(1993)11362359
Article copyright:
© Copyright 1993 American Mathematical Society
