Abstract
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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 1, pp. 169–188, 2011/12.
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Markova, O.V. Classification of matrix subalgebras of length 1. J Math Sci 185, 458–472 (2012). https://doi.org/10.1007/s10958-012-0928-7
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DOI: https://doi.org/10.1007/s10958-012-0928-7