Lie algebras associated with derivation-simple algebras

Yucai Su
Shanghai Jiaotong University

A classification of the pairs $(A,D)$ is obtained, where $A$ is  a
commutative associative algebra with an identity element over an
algebraically closed field of characteristic zero and $D$ is a finite
dimensional subspace of locally-finite commuting derivations of
$A$ such that $A$ is $D$-simple. Such pairs $(A,D)$ are the fundamental
ingredients of constructing Lie algebras of generalized Cartan type.
>From the such pairs $(A,D)$, some new infinite-dimensional simple Lie
algebras can be constructed, which are in general not finitely graded.