Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations
We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformatio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210759 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations. Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites and Irina Shchepochkina. SIGMA 16 (2020), 089, 101 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736444029665280 |
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| author | Bouarroudj, Sofiane Grozman, Pavel Lebedev, Alexei Leites, Dimitry Shchepochkina, Irina |
| author_facet | Bouarroudj, Sofiane Grozman, Pavel Lebedev, Alexei Leites, Dimitry Shchepochkina, Irina |
| citation_txt | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations. Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites and Irina Shchepochkina. SIGMA 16 (2020), 089, 101 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new.
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| first_indexed | 2026-04-17T16:38:24Z |
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| id | nasplib_isofts_kiev_ua-123456789-210759 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:38:24Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Bouarroudj, Sofiane Grozman, Pavel Lebedev, Alexei Leites, Dimitry Shchepochkina, Irina 2025-12-17T14:27:54Z 2020 Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations. Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites and Irina Shchepochkina. SIGMA 16 (2020), 089, 101 pages 1815-0659 2020 Mathematics Subject Classification: 17B50;17B20;70F25 arXiv:1510.07255 https://nasplib.isofts.kiev.ua/handle/123456789/210759 https://doi.org/10.3842/SIGMA.2020.089 We overview the classifications of simple finite-dimensional modular Lie algebras. In characteristic 2, their list is wider than that in other characteristics; e.g., it contains desuperizations of modular analogs of complex simple vectorial Lie superalgebras. We consider odd parameters of deformations. For all 15 Weisfeiler gradings of the 5 exceptional families, and one Weisfeiler grading for each of 2 serial simple complex Lie superalgebras (with 2 exceptional subseries), we describe their characteristic-2 analogs - new simple Lie algebras. Descriptions of several of these analogs, and of their desuperizations, are far from obvious. One of the exceptional simple vectorial Lie algebras is a previously unknown deform (the result of a deformation) of the characteristic-2 version of the Lie algebra of divergence-free vector fields; this is a new simple Lie algebra with no analogs in characteristics distinct from 2. In characteristic 2, every simple Lie superalgebra can be obtained from a simple Lie algebra by one of the two methods described in arXiv:1407.1695. Most of the simple Lie superalgebras thus obtained from simple Lie algebras we describe here are new. We thank S. Skryabin for providing us with [69] and elucidations. We heartily thank the referees, especially the one who wrote 26 pages of constructive comments, for their help; their suggestions considerably improved and clarified the exposition. S.B. and D.L. were partly supported by the grant AD 065 NYUAD. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations Article published earlier |
| spellingShingle | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations Bouarroudj, Sofiane Grozman, Pavel Lebedev, Alexei Leites, Dimitry Shchepochkina, Irina |
| title | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations |
| title_full | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations |
| title_fullStr | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations |
| title_full_unstemmed | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations |
| title_short | Simple Vectorial Lie Algebras in Characteristic 2 and their Superizations |
| title_sort | simple vectorial lie algebras in characteristic 2 and their superizations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210759 |
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