#### Title

ASSOCIATING GEOMETRY to the LIE SUPERALGEBRA sl(1|1) and to the COLOR LIE ALGEBRA sl^{c}_{2}(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

#### Recommended Citation

Sierra, Susan J.; Špenko, Špela; Vancliff, Michaela; Veerapen, Padmini; and Wiesner, Emilie, "ASSOCIATING GEOMETRY to the LIE SUPERALGEBRA sl(1|1) and to the COLOR LIE ALGEBRA sl^{c}_{2}(k)" (2019). *Faculty Articles Indexed in Scopus*. 262.

https://digitalcommons.ithaca.edu/scopus_articles/262