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

Sofiane Bouarroudj; Quentin Ehret; Yoshiaki Maeda

doi:10.3842/SIGMA.2023.070

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

Sofiane Bouarroudj, Quentin Ehret, Yoshiaki Maeda

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	070
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	19
DOIs	https://doi.org/10.3842/SIGMA.2023.070
State	Published - 2023

Keywords

double extension
quasi-Frobenius Lie (super)algebra
restricted Lie (super)algebra

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2023.070

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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 = "double extension, quasi-Frobenius Lie (super)algebra, restricted Lie (super)algebra",

author = "Sofiane Bouarroudj and Quentin Ehret and Yoshiaki Maeda",

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language = "English (US)",

volume = "19",

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AU - Bouarroudj, Sofiane

AU - Ehret, Quentin

AU - Maeda, Yoshiaki

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - double extension

KW - quasi-Frobenius Lie (super)algebra

KW - restricted Lie (super)algebra

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

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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