Classical \(r\)-matrices for the \(\text{osp}(2|2)\) Lie superalgebra (Q2737935)

The author considers the \(\text{osp}(2|2)\) Lie superalgebra \(G\). He finds all Lie supercoalgebra structures on \(G\) which make \(G\) a Lie superbialgebra. They are all of coboundary type, given by an element \(r\) of \(G\wedge G\). The author determines the automorphism group of \(G\), and then classifies the coboundaries \(\delta r\) up to the equivalence given by the action of this group on \(G\wedge G\). There turn out to be 21 inequivalent such \(r\). Analogous results are obtained for the \(\text{osp}(1|2)\oplus {\mathfrak u}(1)\) super Lie bialgebra structures. There are 7 inequivalent ones. The methods used involved a computer and a symbolic algebra program REDUCE.