Representations of $asl_2$

Sophie Morier-Genoud

paper

Representations of $a s l_{2}$

arXiv:0808.2997

Abstract

We study representations of the simple Lie antialgebra $a s l_{2}$ introduced by Ovsienko. We show that representations of $a s l_{2}$ are closely related to the famous ghost Casimir element of the universal enveloping algebra $os p (1∣2)$ . We prove that $a s l_{2}$ has no non-trivial finite-dimensional representations; we define and classify some particular infinite-dimensional representations that we call weighted representations.

17 pages

Representations of asl2​

Abstract

Representations of $a s l_{2}$