Combinatorial structures and Lie algebras of upper triangular matrices

Combinatorial structures and Lie algebras of upper triangular matrices

This work shows how to associate the Lie algebra h n , of upper triangular matrices, with a specific combinatorial structure of dimension 2 , for n ∈ N . The properties of this structure are analyzed and characterized. Additionally, the results obtained here are applied to obtain faithful representa...

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Veröffentlicht in:Applied mathematics letters 2012-03, Vol.25 (3), p.514-519
Hauptverfasser: Ceballos, M., Núñez, J., Tenorio, A.F.
Format: Artikel
Sprache:eng
Schlagworte:
Abelian subalgebras
Combinatorial analysis
Combinatorial structures
Faithful matrix representation
Lie groups
Mathematical analysis
Matrices
Matrix methods
Maximal abelian dimension
Representations
Solvable Lie algebras
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Zusammenfassung:This work shows how to associate the Lie algebra h n , of upper triangular matrices, with a specific combinatorial structure of dimension 2 , for n ∈ N . The properties of this structure are analyzed and characterized. Additionally, the results obtained here are applied to obtain faithful representations of solvable Lie algebras.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2011.09.049