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Simple Lie algebras of small characteristic VI. Completion of the classification
- Source :
-
Journal of Algebra . Nov2008, Vol. 320 Issue 9, p3559-3604. 46p. - Publication Year :
- 2008
-
Abstract
- Abstract: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic . It is proved in this paper that if the p-envelope of adL in DerL contains a torus of maximal dimension whose centralizer in adL acts nontriangulably on L, then and L is isomorphic to one of the Melikian algebras . In conjunction with [A. Premet, H. Strade, Simple Lie algebras of small characteristic V. The non-Melikian case, J. Algebra 314 (2007) 664–692, Theorem 1.2], this implies that, up to isomorphism, any finite-dimensional simple Lie algebra over an algebraically closed field of characteristic is either classical or a filtered Lie algebra of Cartan type or a Melikian algebra of characteristic 5. This result finally settles the classification problem for finite-dimensional simple Lie algebras over algebraically closed fields of characteristic . [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*LINEAR algebra
*SET theory
*AGGREGATED data
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 320
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 34656871
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2008.08.012