Simple Lie algebras which generalize Witt algebras

Abstract

We introduce a new class of simple Lie algebras $W(n,m)$ that generalize the Witt algebra by using "exponential" functions, and also a subalgebra $W^{\ast }(n,m)$ thereof; and we show each derivation of $W^{\ast }(1,0)$ can be written as a sum of an inner derivation and a scalar derivation. The Lie algebra $W(n,m)$ is $Z$-graded and is infinite growth.