N= 1, 2, 3 ℓ-conformal Galilei superalgebras

Abstract

The issue of constructing N = 1, 2, 3 supersymmetric extensions of the ℓ-conformal Galilei algebra is reconsidered following the approach in [27]. Drawing a parallel between acceleration generators entering the superalgebra and irreducible supermultiplets of d = 1, N-extended superconformal group, a new N = 1 ℓ-conformal Galilei superalgebra, two new N = 2 variants, and two new N = 3 versions are built. Realisations in terms of differential operators in superspace are given.