Possible Supersymmetric Kinematics

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 ${\mathfrak{p}}_2$ ${\mathfrak{h}}_{-}$, ${\mathfrak{p}}^{\prime }$, ${\mathfrak{c}}_2$ and ${\mathfrak{g}}^{\prime }$ algebras, in addition to ${\mathfrak{d}}_{-}$, $\mathfrak{p}$, ${\mathfrak{n}}_{-}$, $\mathfrak{g}$ and $\mathfrak{c}$ algebras, have supersymmetric extension, while ${\mathfrak{n}}_{-2}$, ${\mathfrak{g}}_2$ and ${\mathfrak{g}}_2^{\prime }$ algebras have no supersymmetric extension. The connections among the superalgebras are established.

References in corpus (2)

• Geometries for Possible Kinematics
• Geometries with the second Poincaré symmetry

Cited by in corpus (3)

• Kinematical superspaces
• Generalised Bargmann Superalgebras
• Kaluza-Klein reductions of maximally supersymmetric five-dimensional lorentzian spacetimes