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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2023, том 19, 070, 29 стр. (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

Аннотация: 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.

Ключевые слова: restricted Lie (super)algebra, quasi-Frobenius Lie (super)algebra, double extension.

MSC: 17B50, 17B20

Поступила: 31 января 2023 г.; в окончательном варианте 11 сентября 2023 г.; опубликована 28 сентября 2023 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2023.070


ArXiv: 2301.12385


© МИАН, 2024