Solvable Lie algebras derived from Lie hyperalgebras (original) (raw)

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 Sn-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 Sn using the notion of Sn-part. 2010 MSC: 17B60, 17B99, 20N20.