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Lieven Le Bruyn and S. P. Smith
Proceedings of the American Mathematical Society
Vol. 118, No. 3 (Jul., 1993), pp. 725-730
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160112
Page Count: 6
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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 U(sl(2, C)) are in bijection with the lines lying on the quadrics that are the (closures of the) conjugacy classes in sl(2, C). Furthermore, these line modules are the homogenization of the Verma modules for sl(2, C).
Proceedings of the American Mathematical Society © 1993 American Mathematical Society