On varieties of Lie algebras not containing a three-dimensional simple algebra

S. P. Mishchenko


Abstract: It is proved that in the case of zero characteristic of the ground field a variety of Lie algebras not containing a 3-dimensional simple algebra is solvable in the following cases:
1) The variety has a distributive lattice of subvarieties.
2) The variety satisfies all the identities of the infinite-dimensional Witt algebra.

UDC: 519.4

MSC: Primary 17B30; Secondary 08B15, 17B65

Received: 16.07.1990

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1993, 76:1, 189–197

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