FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 1, PAGES 169-188

**Classification of matrix subalgebras of
length $1$**

O. V. Markova

Abstract

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We define the length of a finite system of generators of
a given algebra $\$\; \backslash mathcal\; A\; \$$ as the smallest number $k$ such that words of length
not greater than $k$ generate $\$\; \backslash mathcal\; A\; \$$ 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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k111/k11110h.htm

Last modified: January 31, 2012