Abstract
Recently we have investigated Lie algebras and abelian Lie algebras derived from Lie hyperalgebras using the fundamental relations L and A , respectively. In the present paper, continuing this method we obtain solvable Lie algebras from Lie hyperalgebras by S n -relations. We show that ∩ n ≥ 1 S n * is the smallest equivalence relation on a Lie hyperalgebra such that the quotient structure is a solvable Lie algebra. We also provide some necessary and sufficient conditions for transitivity of the relation S n using the notion of S n -part.
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