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- Title
Hom-Lie Superalgebras in Characteristic 2.
- Authors
Bouarroudj, Sofiane; Makhlouf, Abdenacer
- 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 α k -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.
- Subjects
COHOMOLOGY theory; LIE algebras; STRUCTURAL analysis (Engineering); ALGEBRA
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 24, p4955
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11244955