Kinematical superspaces

Abstract

We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and simplifies many of the calculations, we find a list of $43$ isomorphism classes of Lie superalgebras, some with parameters, whose (nontrivial) central extensions are also determined. We then classify their corresponding simply-connected homogeneous $(4|4)$-dimensional superspaces, resulting in a list of $27$ homogeneous superspaces, some with parameters, all of which are reductive. We determine the invariants of low rank and explore how these superspaces are related via geometric limits.