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

摘要

In this paper, the maximal abelian dimension is algorithmically andcomputationally studied for the Lie algebra hn, of n×n upper-triangularmatrices. More concretely, we define an algorithm to compute abeliansubalgebras of hn besides programming its implementation with thesymbolic computation package MAPLE. The algorithm returns a maximalabelian subalgebra of hn and, hence, its maximal abelian dimension.The order n of the matrices hn is the unique input needed to obtainthese subalgebras. Finally, a computational study of the algorithm ispresented and we explain and comment some suggestions and commentsrelated to how it works.