N $$ \mathcal{N} $$ = 1, 2, 3 ℓ-conformal Galilei superalgebras

Abstract

Abstract The issue of constructing N $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ -extended superconformal group, a new N $$ \mathcal{N} $$ = 1 ℓ-conformal Galilei superalgebra, two new N $$ \mathcal{N} $$ = 2 variants, and two new N $$ \mathcal{N} $$ = 3 versions are built. Realisations in terms of differential operators in superspace are given.

Keywords

• Extended Supersymmetry
• Conformal and W Symmetry