Homogenized

Authors:
Lieven Le Bruyn and S. P. Smith

Journal:
Proc. Amer. Math. Soc. **118** (1993), 725-730

MSC:
Primary 16W50; Secondary 17B37

DOI:
https://doi.org/10.1090/S0002-9939-1993-1136235-9

MathSciNet review:
1136235

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 .

**[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. 33-85. MR**1086882 (92e:14002)****[3]**V. Ginsburg,*Characteristic varieties and vanishing cycles*, Invent. Math.**84**(1986), 327-402. MR**833194 (87j:32030)****[4]**R. Hartshorne,*Algebraic geometry*, Springer-Verlag, 1977. MR**0463157 (57:3116)****[5]**T. Levasseur,*Some properties of non-commutative 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).

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16W50,
17B37

Retrieve articles in all journals with MSC: 16W50, 17B37

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1136235-9

Article copyright:
© Copyright 1993
American Mathematical Society