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Finite-dimensional simple lie algebras with subalgebra lattice of length 3

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Abstract

Lie algebras with subalgebra lattice of length 2 are well known. For studying the subalgebra lattice of a greater length one needs some information on Lie algebras with subalgebra lattice of length 3. We show that there exist four types of finite-dimensional simple Lie algebras over a field of characteristic 0 or a perfect field of prime characteristic greater than 5 such that the length of their subalgebra lattices equals 3.

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Authors and Affiliations

  1. Ural Federal University, ul. Mira 19, Ekaterinburg, 620002, Russia

    A. G. Gein

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  1. A. G. Gein
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Correspondence to A. G. Gein.

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Original Russian Text © A.G. Gein, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 10, pp. 74–78.

Submitted by L.N. Shevrin

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Gein, A.G. Finite-dimensional simple lie algebras with subalgebra lattice of length 3. Russ Math. 56, 62–65 (2012). https://doi.org/10.3103/S1066369X12100064

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  • DOI: https://doi.org/10.3103/S1066369X12100064

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