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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 070, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.070 (Mi sigma1965) 		 
Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras

Sofiane Bouarroudja, Quentin Ehretb, Yoshiaki Maedac

a Division of Science and Mathematics, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates
b University of Haute-Alsace, IRIMAS UR 7499, F-68100 Mulhouse, France
c Tohoku Forum for Creativity, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Japan
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DOI: https://doi.org/10.3842/SIGMA.2023.070
Abstract: In this paper, we present a method of symplectic double extensions for restricted quasi-Frobenius Lie superalgebras. Certain cocycles in the restricted cohomology represent obstructions to symplectic double extension, which we fully describe. We found a necessary condition for which a restricted quasi-Frobenius Lie superalgebras is a symplectic double extension of a smaller restricted Lie superalgebra. The constructions are illustrated with a few examples.
Keywords: restricted Lie (super)algebra, quasi-Frobenius Lie (super)algebra, double extension.
Received: January 31, 2023; in final form September 11, 2023; Published online September 28, 2023
Document Type: Article
MSC: 17B50, 17B20
Language: English
Citation: Sofiane Bouarroudj, Quentin Ehret, Yoshiaki Maeda, “Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras”, SIGMA, 19 (2023), 070, 29 pp.
Citation in format AMSBIB
\Bibitem{BouEhrMae23}
\by Sofiane~Bouarroudj, Quentin~Ehret, Yoshiaki~Maeda
\paper Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras
\jour SIGMA
\yr 2023
\vol 19
\papernumber 070
\totalpages 29
\mathnet{http://mi.mathnet.ru/sigma1965}
\crossref{https://doi.org/10.3842/SIGMA.2023.070}
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