Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908593088888832 |
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| author | Benayadi, Saïd Bouarroudj, Sofiane Ehret, Quentin |
| author_facet | Benayadi, Saïd Bouarroudj, Sofiane Ehret, Quentin |
| contents | The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2. We show that left-symmetric structures can be queerified if and only if they are left-alternative. Secondly, we present a method of Lagrangian extension of Lie superalgebras in characteristic 2 with a flat torsion-free connection. We show that any strongly polarized quasi-Frobenius Lie superalgebra can be obtained as a Lagrangian extension. Further, we demonstrate that Lagrangian extensions are classified by a certain cohomology space that we introduce. To illustrate our constructions, all Lagrangian extensions in dimension 4 have been described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2 Benayadi, Saïd Bouarroudj, Sofiane Ehret, Quentin Representation Theory 17B50, 17B56, 17B05, 17D25 The purpose of this paper is twofold. First, we introduce the notions of left-symmetric and left alternative structures on superspaces in characteristic 2. We describe their main properties and classify them in dimension 2. We show that left-symmetric structures can be queerified if and only if they are left-alternative. Secondly, we present a method of Lagrangian extension of Lie superalgebras in characteristic 2 with a flat torsion-free connection. We show that any strongly polarized quasi-Frobenius Lie superalgebra can be obtained as a Lagrangian extension. Further, we demonstrate that Lagrangian extensions are classified by a certain cohomology space that we introduce. To illustrate our constructions, all Lagrangian extensions in dimension 4 have been described. |
| title | Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2 |
| topic | Representation Theory 17B50, 17B56, 17B05, 17D25 |
| url | https://arxiv.org/abs/2501.15432 |