FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 4, PAGES 165-197

**Length computation of matrix subalgebras of special type**

O. V. Markova

Abstract

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Let $$**F**
be a field and let $\$\; \backslash mathcal\; A\; \$$ be a finite-dimensional $$**F**-algebra.
We define the length of a finite generating set of this algebra
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 generating sets.
In this article, we give a series of examples of length
computation for matrix subalgebras.
In particular, we evaluate the lengths of certain upper triangular
matrix subalgebras and their direct sums, and the lengths of classical
commutative matrix subalgebras.
The connection between the length of an algebra and the lengths of its
subalgebras is also studied.

Location: http://mech.math.msu.su/~fpm/eng/k07/k074/k07409h.htm

Last modified: November 28, 2007