
TL;DR
This paper explores the representation theory of the Lie antialgebra $asl_2$, revealing its connection to the ghost Casimir element of $osp(1|2)$ and classifying certain infinite-dimensional representations.
Contribution
It establishes the relationship between $asl_2$ representations and the ghost Casimir element, and classifies specific infinite-dimensional weighted representations.
Findings
No non-trivial finite-dimensional representations of $asl_2$
Identification of the connection to the ghost Casimir element
Classification of particular infinite-dimensional weighted representations
Abstract
We study representations of the simple Lie antialgebra introduced by Ovsienko. We show that representations of are closely related to the famous ghost Casimir element of the universal enveloping algebra . We prove that 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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