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अमूर्त

Structures of Γ11 over the prime field Z2

BAI Ruipu, GUO Weiwei and BAI Jin

The 8-dimensional 3-Lie algebra Γ11 over the prime field Z2 is realized by 2-cubic matrix, and the structures of it is studied. It is proved that Γ11 is a solvable but non-nilpotent 3-Lie algebra (Theorem 2.3). The inner derivation algebra ad(Γ11) is a 10-dimensional two-step nilpotent Lie algebra (Theorem 2.5), and the derivation algebra Der(Γ11) with dimension 13 is solvable but non-nilpotent (Theorem 2.6). And the concrete expression of all derivations are given.