Representations of $asl_2$

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 $o s p (1 ∣ 2)$ . 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.

Representations of $a s l_{2}$

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Representations of $a s l_{2}$

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Representations of asl2asl2​

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Representations of asl2asl2​

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Representations of $a s l_{2}$

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Representations of $a s l_{2}$

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