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An Algorithm to Compute Abelian Subalgebras in Linear Algebras of Upper-Triangular Matrices

Authors

CEBALLOS GONZÁLEZ, MANUEL, Nunez, Juan , Tenorio, Angel F.

External publication

Si

Means

AIP Conf. Proc.

Scope

Proceedings Paper

Nature

Científica

JCR Quartile

✗

SJR Quartile

✗

SJR Impact

0.163

Publication date

01/01/2009

ISI

000280417500014

Abstract

This paper deals with the maximal abelian dimension of the Lie algebra h(n) of nxn upper-triangular matrices. Regarding this, we obtain an algorithm which computes abelian subalgebras of h(n) as well as its implementation (and a computational study) by using the symbolic computation package MAPLE, where the order n of the matrices in h(n) is the unique input needed. Let us note that the algorithm also allows us to obtain a maximal abtain subalgebra of h(n).

Keywords

Maximal abelian dimension; solvable Lie algebra; algorithmic procedure; programming