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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,
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