A Class of Solvable Lie Algebras with Triangular Decompositions

Abstract

This article introduces a class of solvable Lie algebras with triangular decompositions. The definition of the triangular decomposition in this article is a slight extension of the one given in [1]. It is proved that each of these Lie algebras is determined by an even integer sequence. The highest weight representations of these Lie algebras are also discussed.

Key Words:

• Lie algebra
• Solvable

2000 Mathematics Subject Classification:

• Primary 17BXX
• Secondary 17B10

ACKNOWLEDGMENTS

Great thanks to my supervisor R. V. Moody and professor Bruce Allison for reading this article and giving many suggestions and comments. Great thanks to the editor and the referee for the valuable suggestions to improve the article.

Notes

Communicated by K. Misra.