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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On quantum spaces of Lie algebras


Authors: Lieven Le Bruyn and Michel Van den Bergh
Journal: Proc. Amer. Math. Soc. 119 (1993), 407-414
MSC: Primary 17B35; Secondary 16W30, 17B37
DOI: https://doi.org/10.1090/S0002-9939-1993-1149975-2
MathSciNet review: 1149975
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Abstract: The homogenization $ H(\mathfrak{g})$ of the enveloping algebra of a finite dimensional Lie algebra $ \mathfrak{g}$ is an Artin-Schelter regular algebra. We characterize $ d$-dimensional linear subspaces in the corresponding quantum space $ {\mathbb{P}_q}(\mathfrak{g})$ as homogenizations of induced representations from codimension $ d$ Lie subalgebras. Furthermore we prove that the point variety has an embedded component iff there is a line, not contained in this point variety.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1149975-2
Article copyright: © Copyright 1993 American Mathematical Society