All Questions

Transferred from MSE where it now received a complete answer. Maybe the following is easy, but I am not an expert in finite-dimensional Lie algebras and was stuck on the following problem. Can ...

For every large enough $m\in\Bbb N$ are there $c=\alpha m$ (for some fixed $\alpha>0$) square matrices $A_1,\dots,A_c$ that commute with each other with nonzero product ($\forall i,j\in\{1,\dots,t\}...