Geodesic
Classification of matrix subalgebras of length~1
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 1, pp. 169-188.

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We define the length of a finite system of generators of a given algebra $\mathcal A$ as the smallest number $k$ such that words of length not greater than $k$ generate $\mathcal A$ as a vector space, and the length of the algebra is the maximum of the lengths of its systems of generators. In this paper, we obtain a classification of matrix subalgebras of length 1 up to conjugation. In particular, we describe arbitrary commutative matrix subalgebras of length 1, as well as those that are maximal with respect to inclusion. 
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O. V. Markova. Classification of matrix subalgebras of length~1. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 1, pp. 169-188. http://geodesic.mathdoc.fr/item/FPM_2012_17_1_a9/

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