`-conformal Galilei algebras

Inequivalent N = 2 supersymmetrizations of the `-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the N = 2 supersymmetry. For non-negative integer and half-integer ` both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N = 2 case coincides with the superalgebra introduced by Masterov, while the chiral N = 2 case is a new superalgebra. We present D-module representations of both superalgebras. Then we investigate the new superalgebra derived from the chiral supermultiplet. It is shown that it admits two types of central extensions, one is found for any d and half-integer ` and the other only for d = 2 and integer `. For each central extension the centrally extended `-superconformal Galilei algebra is realized in terms of its super-Heisenberg subalgebra generators. CBPF-NF-003/13 ∗e-mail: [email protected] †e-mail: [email protected] ‡e-mail: [email protected]