Complete triangular structures and Lie algebras

Abstract

In this paper, we study the families of n-dimensional Lie algebras associated with a combinatorial structure made up of n vertices and with its edges forming a complete simple, undirected graph. Moreover, some properties are characterized for these structures using Lie theory, giving some examples and representations. Furthermore, we also study the type of Lie algebras associated with them in order to get their classification. Finally, we also show an implementation of the algorithmic method used to associate Lie algebras with complete triangular structures.

Keywords:

• triangular configuration
• combinatorial structure
• Lie algebras
• classification
• algorithm

2000 AMS Subject Classifications :

• 17B60
• 05C99
• 05C90
• 17B20
• 17B30

Acknowledgements

The authors earnestly would like to thank the referees for their useful and helpful comments and suggestions, which have allowed us to complete and improve the content of this paper.