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

View as HTML     View as gif image

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.

Main page Contents of the journal News Search

Location: http://mech.math.msu.su/~fpm/eng/k1112/k111/k11110h.htm
Last modified: January 31, 2012