Solvable Lie algebras derived from Lie hyperalgebras

Abstract

Recently in [23], 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.