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Homogenized sl(2)

Lieven Le Bruyn and S. P. Smith
Proceedings of the American Mathematical Society
Vol. 118, No. 3 (Jul., 1993), pp. 725-730
DOI: 10.2307/2160112
Stable URL: http://www.jstor.org/stable/2160112
Page Count: 6
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Homogenized sl(2)
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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 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).

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