Representations of $asl_2$

Details Representations of $asl_2$ Representations of $asl_2$

2008-08-22

arxiv.org/abs/0808.2997v2

Mathematics

Representation Theory

17 pages

Scientific paper

We study representations of the simple Lie antialgebra $asl_2$ introduced by Ovsienko. We show that representations of $asl_2$ are closely related to the famous ghost Casimir element of the universal enveloping algebra $osp(1|2)$. We prove that $asl_2$ has no non-trivial finite-dimensional representations; we define and classify some particular infinite-dimensional representations that we call weighted representations.

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