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Simple \(n\)-Lie algebras. (English. Russian original) Zbl 0930.17004

Algebra Logika 38, No. 3, 334-353 (1999); translation in Algebra Logic 38, No. 3, 181-192 (1999).
In 1993 [see Thesis, Univ. GHS Siegen (1993; Zbl 0841.17002)] Ling Wuxue announced a classification of all simple finite-dimensional \(n\)-Lie algebras over any field of zero characteristic. Now the most important problem in the theory is the classification of \(n\)-Lie algebras over fields of nonzero characteristic.
The author gives two examples of simple \(n\)-Lie algebras over a field of nonzero characteristic.

MSC:

17A42 Other \(n\)-ary compositions \((n \ge 3)\)
17B99 Lie algebras and Lie superalgebras

Citations:

Zbl 0841.17002
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