Diagonal reduction algebra for $$\mathfrak{osp}(1|2)$$

Abstract

The problem of providing complete presentations of reduction algebras associated to a pair of Lie algebras $$( \mathfrak{G} , \mathfrak{g} )$$ has previously been considered by Khoroshkin and Ogievetsky in the case of the diagonal reduction algebra for $$\mathfrak{gl}(n)$$ . In this paper, we consider the diagonal reduction algebra of the pair of Lie superalgebras $$( \mathfrak{osp}(1|2) \times \mathfrak{osp}(1|2) , \mathfrak{osp}(1|2) )$$ as a double coset space having an associative $$ \mathrel{\scriptstyle\lozenge} $$ -product and give a complete presentation in terms of generators and relations. We also provide a PBW basis for this reduction algebra along with Casimir-like elements and a subgroup of automorphisms.