<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a maximal abelian subalgebra of hn and, hence, its maximal abelian dimension. The order n of the matrices hn is the unique input needed to obtain these subalgebras. Finally, a computational study of the algorithm is presented and we explain and comment some suggestions and comments related to how it works. </abstract>

In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More concretely, we define an algorithm to compute abelian subalgebras of hn besides programming its implementation with the symbolic computation package MAPLE. The algorithm returns a maximal abelian subalgebra of hn and, hence, its maximal abelian dimension. The order n of the matrices hn is the unique input needed to obtain these subalgebras. Finally, a computational study of the algorithm is presented and we explain and comment some suggestions and comments related to how it works.

Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, the maximal abelian dimension is algorithmically and computationally studied for the Lie algebra hn, of n×n upper-triangular matrices. More...

Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

Published Online: Sep 21, 2017

Page range: 137 - 147

Received: Sep 16, 2014

Accepted: Feb 16, 2015

DOI: https://doi.org/10.1515/auom-2016-0032

Keywords
Maximal abelian dimension, solvable Lie algebra, algorithm

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective

Published Online: Sep 21, 2017

Page range: 137 - 147

Received: Sep 16, 2014

Accepted: Feb 16, 2015

DOI: https://doi.org/10.1515/auom-2016-0032

KeywordsMaximal abelian dimension, solvable Lie algebra, algorithm

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Maximal abelian dimension, solvable Lie algebra, algorithm