A Class of Nongraded Simple Lie Algebras

Abstract

Nongraded simple Lie algebras appear naturally in mathematical physics. In this paper, a new class of nongraded simple Lie algebras are presented based on the pairs (𝒜, 𝒟) consisting of a commutative associative unital algebra 𝒜 and a finite dimensional commutative derivation subalgebra 𝒟 such that 𝒜 is 𝒟-simple. The isomorphism classes of these nongraded Lie algebras are also determined and the structure space of these algebras is given explicitly.