Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
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| Creator |
Bouarroudj, S.
Grozman, P. Leites, D. |
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| Description |
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the corresponding Lie superalgebra is simple otherwise the quotient of the derived Lie superalgebra modulo center is simple (if its rank is greater than 1). Eleven new exceptional simple modular Lie superalgebras are discovered. Several features of classic notions, or notions themselves, are clarified or introduced, e.g., Cartan matrix, several versions of restrictedness in characteristic 2, Dynkin diagram, Chevalley generators, and even the notion of Lie superalgebra if the characteristic is equal to 2. Interesting phenomena in characteristic 2: (1) all simple Lie superalgebras with Cartan matrix are obtained from simple Lie algebras with Cartan matrix by declaring several (any) of its Chevalley generators odd; (2) there exist simple Lie superalgebras whose even parts are solvable. The Lie superalgebras of fixed points of automorphisms corresponding to the symmetries of Dynkin diagrams are also listed and their simple subquotients described.
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| Date |
2019-02-19T17:29:38Z
2019-02-19T17:29:38Z 2009 |
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| Type |
Article
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| Identifier |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix / S. Bouarroudj, P. Grozman, D. Leites // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 54 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 17B50; 70F25 http://dspace.nbuv.gov.ua/handle/123456789/149116 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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