This article is cited in 2 papers

Brief communications

Finite-dimensional simple Lie algebras with a subalgebra lattice of length 3

A. G. Gein

Chair of Algebra and Discrete Mathematics, Ural Federal University, Ekaterinburg, Russia

Abstract: Lie algebras with a subalgebra lattice of length 2 are well-known. To study a subalgebra lattice of greater length, it is useful to get some information on Lie algebras with a subalgebra lattice of length 3. We show that a finite-dimensional simple Lie algebra over a field of characteristic 0 or a perfect field of prime characteristic greater than 5 whose subalgebra lattice has length 3 may be one of four types.

Keywords: simple Lie algebras, subalgebra lattices, minimal algebras.

UDC: 512.554

Presented by the member of Editorial Board: L. N. Shevrin
Received: 24.02.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:10, 62–65

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