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Some algebraic properties of the supersymmetric extension of GCA in 2d

In this paper, we study some algebraic properties of the supersymmetric extension of Galilean conformal algebra (SGCA) in 2d introduced by I Mandal. The derivations, the central extensions, and the automorphisms of the SGCA are determined explicitly. Moreover, we present a natural realization of the SGCA in terms of the affinization of a Balinsky–Novikov superalgebra in dimension 2|2. Using this realization, we construct some vertex superalgebras and modules associated to the representations for the SGCA.