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

被引：2
|
作者：
Bouarroudj, Sofiane [1 ]
Ehret, Quentin [2 ]
Maeda, Yoshiaki [3 ]
机构：
[1] NYU Abu Dhabi, Div Sci & Math, POB 129188, Abu Dhabi, U Arab Emirates
[2] Univ Haute Alsace, IRIMAS UR 7499, F-68100 Mulhouse, France
[3] Tohoku Univ, Tohoku Forum Creat, 2-1-1 Katahira,Aoba Ku, Sendai, Japan
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2023年 / 19卷
关键词：
restricted Lie (super)algebra; quasi-Frobenius Lie (super)algebra; double exten- sion; ENVELOPING-ALGEBRAS; COHOMOLOGY; INVARIANT; REPRESENTATIONS; CLASSIFICATION; SUPERALGEBRAS; IDENTITIES; FORMS;
D O I：
10.3842/SIGMA.2023.070
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：29
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