Mathematica Eterna
Open Access

Abstract

3-Lie algebra Γ21 over the prime field Z2

BAI Ruipu, LIN Lixin and BAI Jin

The 8-dimensional 3-Lie algebra Γ21 over the prime field Z2 is constructed by 2-cubic matrix, and the structures of it is studied. It is proved that Γ21 is a solvable but non-nilpotent 3-Lie algebra. The inner derivation algebra ad(Γ21) is a 12-dimensional solvable but nonnilpotent Lie algebra, and the derivation algebra Der(Γ21) with dimension 17 is unsolvable. And the concrete expression of all derivations are given.