Kinematical superspaces
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2019)008 |
| _version_ | 1811294710082306048 |
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| author | José Figueroa-O’Farrill Ross Grassie |
| author_facet | José Figueroa-O’Farrill Ross Grassie |
| author_sort | José Figueroa-O’Farrill |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T05:21:30Z |
| format | Article |
| id | doaj.art-dda35a9a287947999d6d2bc1a56cf2aa |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-13T05:21:30Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-dda35a9a287947999d6d2bc1a56cf2aa2022-12-22T03:00:45ZengSpringerOpenJournal of High Energy Physics1029-84792019-11-0120191117610.1007/JHEP11(2019)008Kinematical superspacesJosé Figueroa-O’Farrill0Ross Grassie1Maxwell Institute and School of Mathematics, The University of EdinburghMaxwell Institute and School of Mathematics, The University of EdinburghAbstract 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.http://link.springer.com/article/10.1007/JHEP11(2019)008Space-Time SymmetriesSuperspaces |
| spellingShingle | José Figueroa-O’Farrill Ross Grassie Kinematical superspaces Journal of High Energy Physics Space-Time Symmetries Superspaces |
| title | Kinematical superspaces |
| title_full | Kinematical superspaces |
| title_fullStr | Kinematical superspaces |
| title_full_unstemmed | Kinematical superspaces |
| title_short | Kinematical superspaces |
| title_sort | kinematical superspaces |
| topic | Space-Time Symmetries Superspaces |
| url | http://link.springer.com/article/10.1007/JHEP11(2019)008 |
| work_keys_str_mv | AT josefigueroaofarrill kinematicalsuperspaces AT rossgrassie kinematicalsuperspaces |