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.

Key Words:

• Nongraded Lie algebra
• Isomorphism class
• Structure space

Mathematics Subject Classification (1991):

• 17B05
• 17B20
• 17B65
• 17B68

Acknowledgments

The authors would like to thank Prof. Xiaoping Xu for discussions and suggestion of investigating this problem. Supported by a NSF grant 10171064 of China and an EYTP grant of MOE of China.

Notes

^#Communicated by K. Misra.