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Keywords = Hom-Lie superalgebra

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29 pages, 412 KiB  
Article
Hom-Lie Superalgebras in Characteristic 2
by Sofiane Bouarroudj and Abdenacer Makhlouf
Mathematics 2023, 11(24), 4955; https://doi.org/10.3390/math11244955 - 14 Dec 2023
Cited by 2 | Viewed by 4353
Abstract
The main goal of this paper was to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, and αk-derivations and provide a classification in low dimension. We introduce another notion of restrictedness on Hom-Lie [...] Read more.
The main goal of this paper was to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, and αk-derivations and provide a classification in low dimension. We introduce another notion of restrictedness on Hom-Lie algebras in characteristic 2, different from the one given by Guan and Chen. This definition is inspired by the process of the queerification of restricted Lie algebras in characteristic 2. We also show that any restricted Hom-Lie algebra in characteristic 2 can be queerified to give rise to a Hom-Lie superalgebra. Moreover, we developed a cohomology theory of Hom-Lie superalgebras in characteristic 2, which provides a cohomology of ordinary Lie superalgebras. Furthermore, we established a deformation theory of Hom-Lie superalgebras in characteristic 2 based on this cohomology. Full article
(This article belongs to the Section A: Algebra and Logic)
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