Bulletin of the
Korean Mathematical Society BKMS

Kawamoto generalized the Witt algebra using $F[x_1^{\pm 1},$ $\cdots ,x_n^{\pm 1}]$ instead of $F[x_1,\cdots ,x_n]$. We construct the generalized Witt algebra $W_{g,h,n}$ by using additive mappings $g, h$ from a set of integers into a field $F$ of characteristic zero. We show that the Lie algebra $W_{g,h,n}$ is simple if $g$ and $h$ are injective, and also the Lie algebra $W_{g,h,n}$ has no ad-diagonalizable elements.

Keywords: simple Lie algebras, Lie derivation, Lie automorphism

MSC numbers: Primary 17B40, 17B65; Secondary 17B56, 17B68