Kinematical superspaces

Abstract

Abstract We classify N =1 d = 4 kinematical and aristotelian Lie superalgebras with spa- tial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quater- nionic 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 pa- rameters, 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.

Keywords

• Space-Time Symmetries
• Superspaces