Z 2 × Z 2 generalizations of N=1 superconformal Galilei algebras and their representations

Abstract

We introduce two classes of novel color superalgebras of Z2×Z2 grading. This is done by realizing members of each class within the universal enveloping algebra of the N=1 supersymmetric extension of the conformal Galilei algebra. This allows us to upgrade any representation of the super conformal Galilei algebras to a representation of the Z2×Z2 graded algebra. As an example, boson-fermion Fock space representation of one class is given. We also provide a vector field realization of members of the other class by using a generalization of the Grassmann calculus to Z2×Z2 graded setting.