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arXiv · 1808.09112

$ \mathbb{Z}_2 \times \mathbb{Z}_2 $ generalizations of ${\cal N} = 1$ superconformal Galilei algebras and their representations

N. Aizawa·P. S. Isaac·J. Segar
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Abstract

We introduce two classes of novel color superalgebras of $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ grading. This is done by realizing members of each in the universal enveloping algebra of the ${\cal N}=1$ 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 $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ 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 $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ graded setting.

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N. Aizawa, P. S. Isaac, J. Segar. 2018-08-28. $ \mathbb{Z}_2 \times \mathbb{Z}_2 $ generalizations of ${\cal N} = 1$ superconformal Galilei algebras and their representations. https://doi.org/10.1063/1.5054699

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