Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 070, 29 pages      arXiv:2301.12385      https://doi.org/10.3842/SIGMA.2023.070
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

Symplectic Double Extensions for Restricted Quasi-Frobenius Lie (Super)Algebras

Sofiane Bouarroudj a, Quentin Ehret b and Yoshiaki Maeda c
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

Received January 31, 2023, in final form September 11, 2023; Published online September 28, 2023

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.

Key words: restricted Lie (super)algebra; quasi-Frobenius Lie (super)algebra; double extension.

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