N = 2 Galilean superconformal algebras with central extension

N = 2 Supersymmetric extensions of Galilean conformal algebra (GCA), specified by spin \ell and dimension of space d, are investigated. Duval and Horvathy showed that the \ell = 1/2 GCA has two types of supersymmetric extensions, called standard and exotic. Recently, Masterov intorduced a centerless super-GCA for arbitrary \ell wchich corresponds to the standard extension. We show that the Masterov's super-GCA has two types of central extensions depending on the parity of 2\ell. We then introduced a novel super-GCA for arbitrary \ell corresponding to the exotic extension. It is shown that the exotic superalgebra also has two types of central extensions depending on the parity of 2\ell. Furthermore, we give a realization of the standard and exotic super-GCA's in terms of their subalgebras. Finally, we present a N = 1 supersmmetric extension of GCA with central extensions.Comment: 14 pages, no figure, version published in J. Phys. A., Texts updated, new reference

Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs

We construct, for any given $\ell = \frac{1}{2} + {\mathbb N}_0,$ the second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. The generators are obtained by a coset construction and the PDEs are constructed by standard Lie symmetry technique. It is observed that the invariant PDEs have significant difference for $\ell > \frac{3}{2}.$Comment: 22pages, 3figure