Hom-Lie Superalgebras in Characteristic 2
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/24/4955 |
| _version_ | 1797380160477986816 |
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| author | Sofiane Bouarroudj Abdenacer Makhlouf |
| author_facet | Sofiane Bouarroudj Abdenacer Makhlouf |
| author_sort | Sofiane Bouarroudj |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>α</mi><mi>k</mi></msup></semantics></math></inline-formula>-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. |
| first_indexed | 2024-03-08T20:34:19Z |
| format | Article |
| id | doaj.art-e781fcec36eb4ac28357a3261ddf84e9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T20:34:19Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e781fcec36eb4ac28357a3261ddf84e92023-12-22T14:23:25ZengMDPI AGMathematics2227-73902023-12-011124495510.3390/math11244955Hom-Lie Superalgebras in Characteristic 2Sofiane Bouarroudj0Abdenacer Makhlouf1Division of Science and Mathematics, New York University Abu Dhabi, Abu Dhabi P.O. Box 129188, United Arab EmiratesIRIMAS—Mathematics Department, University of Haute Alsace, 68093 Mulhouse, FranceThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>α</mi><mi>k</mi></msup></semantics></math></inline-formula>-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.https://www.mdpi.com/2227-7390/11/24/4955Hom-Lie superalgebramodular Lie superalgebracharacteristic 2representationqueerificationcohomology |
| spellingShingle | Sofiane Bouarroudj Abdenacer Makhlouf Hom-Lie Superalgebras in Characteristic 2 Mathematics Hom-Lie superalgebra modular Lie superalgebra characteristic 2 representation queerification cohomology |
| title | Hom-Lie Superalgebras in Characteristic 2 |
| title_full | Hom-Lie Superalgebras in Characteristic 2 |
| title_fullStr | Hom-Lie Superalgebras in Characteristic 2 |
| title_full_unstemmed | Hom-Lie Superalgebras in Characteristic 2 |
| title_short | Hom-Lie Superalgebras in Characteristic 2 |
| title_sort | hom lie superalgebras in characteristic 2 |
| topic | Hom-Lie superalgebra modular Lie superalgebra characteristic 2 representation queerification cohomology |
| url | https://www.mdpi.com/2227-7390/11/24/4955 |
| work_keys_str_mv | AT sofianebouarroudj homliesuperalgebrasincharacteristic2 AT abdenacermakhlouf homliesuperalgebrasincharacteristic2 |