  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 $n\geq 3$ and
provide a problem.
