Abstract
We construct a generalized Witt algebra W(g p , h p , n) and a Hamiltonian algebra $$ \overline{H(g_{2n}, h_{2n}, 2n}$$ by using additive maps g p , h p where 1 ≤ p ≤ n from a set of integers into a field of characteristic zero. We show that the Lie algebras W(g p , h p , n). and $$ \overline{H(g_{2n}, h_{2n}, 2n} $$ are simple if g p and h p are injective, and also that the Lie algebras W(g p , h p , n) and $$ \overline{H(g_{2n}, h_{2n}, 2n} $$ have no ad-diagonal elements with respect to the standard basis.
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