  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.
