Wronskians as <i>N</i> -ary brackets in finite-dimensional analogues of sl(2)

Abstract TheWronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras - i.e. for a particular case of L ͚-deformations – for the Lie algebra of vector fields on that one-dimensional affine manifold. We show that thestandard realisation of sl(2) by quadratic-coefficient vector fields is the bottom structurein a sequence of finite-dimensional polynomial algebras 𝕂 N [ x ] with the Wronskians as N -ary brackets; the structure constants are calculated explicitly.