Classification of certain types of maximal matrix subalgebras

2017/04/08 by Eggers, John, Evans, Ron, Van Veen, Mark
#15B33 #16S50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1704.02437

Abstract

Let M_n(K) denote the algebra of n × n matrices over a field K of characteristic zero. A nonunital subalgebra N ⊂ M_n(K) will be called a nonunital intersection if N is the intersection of two unital subalgebras of M_n(K). Appealing to recent work of Agore, we show that for n ≥ 3, the dimension (over K) of a nonunital intersection is at most (n-1)(n-2), and we completely classify the nonunital intersections of maximum dimension (n-1)(n-2). We also classify the unital subalgebras of maximum dimension properly contained in a parabolic subalgebra of maximum dimension in M_n(K).

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