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 Fundam. Prikl. Mat., 2012, Volume 17, Issue 1, Pages 169–188 (Mi fpm1395)

Classification of matrix subalgebras of length 1

O. V. Markova

M. V. Lomonosov Moscow State University

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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English version:
Journal of Mathematical Sciences (New York), 2012, 185:3, 458–472

UDC: 512.643

Citation: O. V. Markova, “Classification of matrix subalgebras of length 1”, Fundam. Prikl. Mat., 17:1 (2012), 169–188; J. Math. Sci., 185:3 (2012), 458–472

Citation in format AMSBIB
\Bibitem{Mar12} \by O.~V.~Markova \paper Classification of matrix subalgebras of length~1 \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 1 \pages 169--188 \mathnet{http://mi.mathnet.ru/fpm1395} \transl \jour J. Math. Sci. \yr 2012 \vol 185 \issue 3 \pages 458--472 \crossref{https://doi.org/10.1007/s10958-012-0928-7} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866320171} 

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This publication is cited in the following articles:
1. O. V. Markova, “Description of algebras of length $1$”, Moscow University Mathematics Bulletin, 68:1 (2013), 74–76
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