Computing abelian subalgebras for linear algebras of upper-triangular matrices from an algorithmic perspective
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 pack...
| Authors: | ; ; |
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2016 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/49657 |
| Online Access: | http://hdl.handle.net/11441/49657 https://doi.org/10.1515/auom-2016-0032 |
| Access Level: | Open access |
| Keyword: | Maximal abelian dimension Solvable Lie algebra Algorithm |
| Summary: | 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. |
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