I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2011/2012, VOLUME 17, NUMBER 1, PAGES 169-188
Classification of matrix subalgebras of
O. V. Markova
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We define the length of a finite system of generators of
a given algebra as the smallest number such that words of length
not greater than generate 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 up to conjugation.
In particular, we describe arbitrary commutative matrix subalgebras of
as well as those that are maximal with respect to inclusion.
Last modified: January 31, 2012