Title

ASSOCIATING GEOMETRY to the LIE SUPERALGEBRA sl(1|1) and to the COLOR LIE ALGEBRA slc2(k)

Document Type

Article

Publication Date

1-1-2019

Abstract

2019 American Mathematical Society In the 1990s, in work of Le Bruyn and Smith and in work of Le Bruyn and Van den Bergh, it was proved that point modules and line modules over the homogenization of the universal enveloping algebra of a finite-dimensional Lie algebra describe useful data associated to the Lie algebra. In particular, in the case of the Lie algebra sl2(C), there is a correspondence between Verma modules and certain line modules that associates a pair (h, φ), where h is a 2-dimensional Lie subalgebra of sl2(C) and φ ∈ h∗ satisfies φ([h, h]) = 0, to a particular type of line module. In this article, we prove analogous results for the Lie superalgebra sl(1|1) and for a color Lie algebra associated to the Lie algebra sl2

Publication Name

Proceedings of the American Mathematical Society

Volume Number

147

First Page

4135

Last Page

4146

Issue Number

10

DOI

10.1090/proc/14647

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