Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov)
Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same multiplicity) and of ranks less than or equal to 8—most needed in an...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211911 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov). Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev and Dimitry Leites. SIGMA 19 (2023), 032, 73 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862624898199846912 |
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| author | Bouarroudj, Sofiane Grozman, Pavel Alexei, Lebedev Leites, Dimitry |
| author_facet | Bouarroudj, Sofiane Grozman, Pavel Alexei, Lebedev Leites, Dimitry |
| citation_txt | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov). Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev and Dimitry Leites. SIGMA 19 (2023), 032, 73 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same multiplicity) and of ranks less than or equal to 8—most needed in an approach to the classification of simple vectorial Lie superalgebras (i.e., Lie superalgebras realized by means of vector fields on a supermanifold),—we list the outer derivations and nontrivial central extensions. When the conjectural answer is clear for the infinite series, it is given for any rank. We also list the outer derivations and nontrivial central extensions of one series of non-symmetric (except when considered in characteristic 2), namely periplectic, Lie superalgebras—the one that preserves the nondegenerate symmetric odd bilinear form, and of the Lie algebras obtained from them by desuperization. We also list the outer derivations and nontrivial central extensions of an analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu. Several results indigenous to positive characteristic are of particular interest, being unlike known theorems for characteristic 0, some results are, moreover, counterintuitive.
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| first_indexed | 2026-03-14T15:16:05Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211911 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T15:16:05Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bouarroudj, Sofiane Grozman, Pavel Alexei, Lebedev Leites, Dimitry 2026-01-16T11:17:56Z 2023 Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov). Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev and Dimitry Leites. SIGMA 19 (2023), 032, 73 pages 1815-0659 2020 Mathematics Subject Classification: 17B50;17B55;17B56;17B20;17B40 arXiv:1307.1858 https://nasplib.isofts.kiev.ua/handle/123456789/211911 https://doi.org/10.3842/SIGMA.2023.032 Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same multiplicity) and of ranks less than or equal to 8—most needed in an approach to the classification of simple vectorial Lie superalgebras (i.e., Lie superalgebras realized by means of vector fields on a supermanifold),—we list the outer derivations and nontrivial central extensions. When the conjectural answer is clear for the infinite series, it is given for any rank. We also list the outer derivations and nontrivial central extensions of one series of non-symmetric (except when considered in characteristic 2), namely periplectic, Lie superalgebras—the one that preserves the nondegenerate symmetric odd bilinear form, and of the Lie algebras obtained from them by desuperization. We also list the outer derivations and nontrivial central extensions of an analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu. Several results indigenous to positive characteristic are of particular interest, being unlike known theorems for characteristic 0, some results are, moreover, counterintuitive. We are thankful to A. Krutov for his help, e.g., for computing several examples (Section 2.3). We are thankful to N. Chebochko and M. Kuznetsov for their helpful discussions of unpublished results pertinent to this paper; to A. Dzhumadildaev, P. Zusmanovich, and Sh. Ibraev for helpful discussions. We are very thankful to the referees, carefully selected by SIGMA, especially one of them, for their constructive criticism. S.B. and D.L. were supported by the grant AD 065 NYUAD. D.L. is thankful to MPIMiS, Leipzig, where he was Sophus-Lie-Professor (2004-07), when a part of the ideas of this paper were conceived, for financial support and the most creative environment. The authors of the main text and A. Krutov, who wrote the Appendix, are grateful to M. Al Barwani, Director of the High Performance Computing resources at New York University Abu Dhabi, for the possibility to perform the difficult computations of this research. Andrey Krutov was supported by the GAČR project 20-17488Y and RVO: 67985840. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) Article published earlier |
| spellingShingle | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) Bouarroudj, Sofiane Grozman, Pavel Alexei, Lebedev Leites, Dimitry |
| title | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) |
| title_full | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) |
| title_fullStr | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) |
| title_full_unstemmed | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) |
| title_short | Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov) |
| title_sort | derivations and central extensions of symmetric modular lie algebras and superalgebras (with an appendix by andrey krutov) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211911 |
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