An algorithm to compute abelian subalgebras in linear algebras of upper-triangular matrices

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

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