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.
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ArXiv ePrint: 1908.11278
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Figueroa-O’Farrill, J., Grassie, R. Kinematical superspaces. J. High Energ. Phys. 2019, 8 (2019). https://doi.org/10.1007/JHEP11(2019)008
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DOI: https://doi.org/10.1007/JHEP11(2019)008