Killing Superalgebras in 2 Dimensions
We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages]. We compute the Spencer cohomology group H²’²(₋; ) and filtered deformations of the non-chiral flat model (Euclidean and Poi...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214202 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Killing Superalgebras in 2 Dimensions. Andrew D.K. Beckett. SIGMA 21 (2025), 082, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862605324084576256 |
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| author | Beckett, Andrew D.K. |
| author_facet | Beckett, Andrew D.K. |
| citation_txt | Killing Superalgebras in 2 Dimensions. Andrew D.K. Beckett. SIGMA 21 (2025), 082, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages]. We compute the Spencer cohomology group H²’²(₋; ) and filtered deformations of the non-chiral flat model (Euclidean and Poincaré) superalgebra for various Dirac currents and show these arise as Killing superalgebras for (imaginary) geometric Killing and skew-Killing spinors in both Riemannian and Lorentzian signature.
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| first_indexed | 2026-03-21T12:22:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214202 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:22:28Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Beckett, Andrew D.K. 2026-02-20T08:03:18Z 2025 Killing Superalgebras in 2 Dimensions. Andrew D.K. Beckett. SIGMA 21 (2025), 082, 16 pages 1815-0659 2020 Mathematics Subject Classification: 17B66; 17B56 arXiv:2410.01765 https://nasplib.isofts.kiev.ua/handle/123456789/214202 https://doi.org/10.3842/SIGMA.2025.082 We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages]. We compute the Spencer cohomology group H²’²(₋; ) and filtered deformations of the non-chiral flat model (Euclidean and Poincaré) superalgebra for various Dirac currents and show these arise as Killing superalgebras for (imaginary) geometric Killing and skew-Killing spinors in both Riemannian and Lorentzian signature. The author would like to thank José Figueroa-O’Farrill, under whose supervision this work was done, for his guidance and patience. Thanks also to Andrea Santi, James Lucietti, C.S. Shahbazi, and the sorely missed Paul de Medeiros for many enlightening conversations and helpful comments. Finally, thanks to the anonymous referees for their comments and suggestions, which greatly improved the quality and clarity of this work. This work was carried out with scholarship funding from the Science and Technology Facilities Council (STFC) and the School of Mathematics at the University of Edinburgh. This work previously appeared as part of the author’s Ph.D. Thesis [3] but has not been published elsewhere. Some changes in notation and terminology have been made for this version to aid comparison with other work, and there are also some minor changes in exposition and corrections. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Killing Superalgebras in 2 Dimensions Article published earlier |
| spellingShingle | Killing Superalgebras in 2 Dimensions Beckett, Andrew D.K. |
| title | Killing Superalgebras in 2 Dimensions |
| title_full | Killing Superalgebras in 2 Dimensions |
| title_fullStr | Killing Superalgebras in 2 Dimensions |
| title_full_unstemmed | Killing Superalgebras in 2 Dimensions |
| title_short | Killing Superalgebras in 2 Dimensions |
| title_sort | killing superalgebras in 2 dimensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214202 |
| work_keys_str_mv | AT beckettandrewdk killingsuperalgebrasin2dimensions |