Classification of matrix subalgebras of length 1

Markova, O.
September 2012
Journal of Mathematical Sciences;Sep2012, Vol. 185 Issue 3, p458
Academic Journal
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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