Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
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...
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| Дата: | 2009 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149116 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491162019-02-20T01:27:15Z Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix Bouarroudj, S. Grozman, P. Leites, D. 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. 2009 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bouarroudj, S. Grozman, P. Leites, D. |
| spellingShingle |
Bouarroudj, S. Grozman, P. Leites, D. Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bouarroudj, S. Grozman, P. Leites, D. |
| author_sort |
Bouarroudj, S. |
| title |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix |
| title_short |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix |
| title_full |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix |
| title_fullStr |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix |
| title_full_unstemmed |
Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix |
| title_sort |
classification of finite dimensional modular lie superalgebras with indecomposable cartan matrix |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149116 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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