Remarks on finite \({\mathcal W}\) algebras. (Q1589224)

The authors study a special class of \(\mathcal W\)-algebras which can occur as the commutant in \({\mathcal U}({\mathfrak G})\) of a subalgebra \({\mathfrak L}\subset {\mathfrak G}\) and which can be used to construct realizations of \({\mathfrak G}\). They give detailed results in case \({\mathfrak G}\) is \(\text{so}(4,2)\), the conformal or the Poincaré algebras and for \(\text{sp}(2,\mathbb R)\) and \(\text{sp}(4,\mathbb R)\) in which case anyonic parameters appear.