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

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 chara...

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Bibliographic Details
Published in:Russian mathematics 2012-10, Vol.56 (10), p.62-65
Main Author: Gein, A. G.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X12100064