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
Date:2025
Main Author: Beckett, Andrew D.K.
Format: Article
Language:English
Published: Інститут математики НАН України 2025
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
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2026-03-21T12:22:28Z
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publisher Інститут математики НАН України
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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