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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