- 23 Downloads
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.
KeywordsSpace-Time Symmetries Superspaces
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
- F. Palumbo, Nonrelativistic Supersymmetry, in Proceedings of the International Conference on Recent Progress in Many Body Theories, International Center for Theoretical Physics, Trieste Italy (1978), pg. 582.Google Scholar
- J.-L. Koszul, Graded manifolds and graded Lie algebras, in Proceedings of the international meeting on geometry and physics, Florence Italy (1982), Pitagora, Bologna Italy (1983), pg. 71.Google Scholar