Simple classical Lie algebras in characteristic 2 and their gradations. II. (English) Zbl 1350.17014
Summary: This paper is a continuation of the authors’ paper [Int. J. Math. Game Theory Algebra 13, No. 3, 239–252 (2003; Zbl 1049.17016)]. We prove Conjecture 5.1 of that paper which gives a characterization of simple Lie algebras of finite dimension of type \(B_{2\ell}\), \(C_{2\ell}\), \(D_{2\ell+1}\), \(E_{7}\) and \(E_{8}\) in terms of some gradations of these algebras over a field of characteristic 2.
MSC:
| 17B50 | Modular Lie (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B20 | Simple, semisimple, reductive (super)algebras |
Citations:
Zbl 1049.17016References:
| [1] | DOI: 10.1142/S0218196701000826 · Zbl 1024.17004 · doi:10.1142/S0218196701000826 |
| [2] | Grishkov M, Algebra 13 pp 239– (2003) |
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