Mathematica Eterna
Open Access

Abstract

3-Lie algebra Γ27 over the prime field Z2

BAI Ruipu and LIN Lixin

In this paper, the 8-dimensional 3-Lie algebra Γ27 over the prime field Z2 is constructed by 2-cubic matrix. It is proved that Γ27 is a solvable but non-nilpotent 3-Lie algebra. The inner derivation algebra ad(Γ27) is an 11-dimensional solvable Lie algebra, and the derivation algebra Der(Γ27) with dimension 18 is solvable but non-nilpotent. And the concrete expression of all derivations are given.