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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Homogenized $ \mathfrak{sl}(2)$

Authors: Lieven Le Bruyn and S. P. Smith
Journal: Proc. Amer. Math. Soc. 118 (1993), 725-730
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 $ U(\mathfrak{s}\mathfrak{l}(2,\mathbb{C}))$ are in bijection with the lines lying on the quadrics that are the (closures of the) conjugacy classes in $ \mathfrak{s}\mathfrak{l}(2,\mathbb{C})$. Furthermore, these line modules are the homogenization of the Verma modules for $ \mathfrak{s}\mathfrak{l}(2,\mathbb{C})$.

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PII: S 0002-9939(1993)1136235-9
Article copyright: © Copyright 1993 American Mathematical Society

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