Possible Supersymmetric Kinematics

preprint2014arXivOpen access

Abstract

The contraction method in different limits to obtain 22 different realizations of kinematical algebras is applied to study the supersymmetric extension of \AdS\ algebra and its contractions. It is shown that p2\frak{p}_2 h−\frak{h}_-, p′\frak{p}', c2\frak{c}_2 and g′\frak{g}' algebras, in addition to d−\frak{d}_-, p\frak{p}, n−\frak{n}_-, g\frak{g} and c\frak{c} algebras, have supersymmetric extension, while n−2\frak{n}_{-2}, g2\frak{g}_2 and g2′\frak{g}'_2 algebras have no supersymmetric extension. The connections among the superalgebras are established.

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