Constructing 3-Lie algebras

Abstract

3-Lie algebras are constructed by Lie algebras, derivations and linear functions, associative commutative algebras, whose involutions and derivations. Then the 3-Lie algebras are obtained from group algebras $F[G]$. An infinite dimensional simple 3-Lie algebra $(A,[,,{]}_{\omega ,{\delta }_0})$ and a non-simple 3-Lie algebra $(A,[,,{]}_{{\omega }_1,\delta })$ are constructed by Laurent polynomials $A=F[t,t^{-1}]$ and its involutions $\omega$ and ${\omega }_1$ and derivations $\delta$ and ${\delta }_0$. At last of the paper, we summarize the methods of constructing $n$-Lie algebras for $n\ge 3$ and provide a problem.

18 pages

References in corpus (3)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's

Cited by in corpus (1)

• Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras