Derivations and 2-Cocycles of Contact Lie Algebras Related to Locally-Finite Derivations

Abstract

Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. Xu introduced a large category of contact simple Lie algebras which are related to locally finite derivations and are in general not finitely graded. The isomorphism classes of these Lie algebras were determined in a previous paper by Xu and Su. In this paper, the derivation algebras and the 2-cohomology groups of these Lie algebras are determined, and it is obtained that the 2-cohomology groups of these Lie algebras are all trivial.

Key Words:

• Lie algebras of contact type
• Structure
• Derivation
• 2-Cocycle

1991 Mathematical Subject Classification:

• Primary 17B65
• Secondary 58F05

Acknowledgments

The authors were supported by NSF grant 10171064 of China and two grants “Excellent Young Teacher Program” and “Trans-Century Training Programme Foundation for the Talents” from Ministry of Education of China.

Notes

^#Communicated by K. Misra.