On Lie algebras derived from Lie hyperalgebras

Solvable Lie algebras derived from Lie hyperalgebras

“…This section is devoted to discuss some preliminary results on Lie algebras obtained from Lie hyperalgebras from [23].…”

“…, g im i only by hyperbracket. Moreover, it is shown that L * is a strongly regular relation on L, which is also the smallest equivalence relation on L such that L/L * is a (fundamental) Lie algebra (see Theorem 3.3 and Corollary 3.4 in [23]).…”

“…A Lie algebra L, over a field F, is said to be abelian, if L (1) = 0. It is easy to see that if the characteristic of F is not 2 and ⌊x, y⌋ = ⌊y, x⌋ for all x, y ∈ L, then L is abelian (see also [23]). In the following results, F is a hyperfield such that the characteristic of the field F/α * is not 2.…”

“…The authors in [23] studied strongly regular relations on Lie hyperalgebras and obtained Lie algebras and abelian Lie algebras from Lie hyperalgebras using the fundamental relations L and A, respectively. Now in this paper, we investigate solvable Lie algebras derived from Lie hyperalgebras by S n -relations (L ⊆ S n ⊆ S 1 = A).…”

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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.

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