Let $A\subseteq M_n(\mathbb{F})$ be an algebra of matrices over $\mathbb{F}$, and suppose it is semi-simple. Is $Z=\{g\in M_n(\mathbb{F})\,|\,gX=Xg\,\forall X\in A\}$ also semisimple?
2026-02-23 02:12:59.1771812779
Is the commutant of a semisimple algebra also semisimple?
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