Generators of Supersymmetric Classical W-Algebras

Abstract

Let \({\mathfrak {g}}\) be a Lie superalgebra of type \(\mathfrak {sl}\) or \(\mathfrak {osp}\) with an odd principal nilpotent element f. We consider a matrix \({\mathcal {A}}_{{\mathfrak {g}},f}\) determined by \({\mathfrak {g}}\) and f and find a generating set of the supersymmetric classical W-algebra \({\mathcal {W}}(\bar{{\mathfrak {g}}},f)\) using the row determinant of \({\mathcal {A}}_{{\mathfrak {g}},f}\).