New classes of examples satisfying the three matrix analog of Gerstenhaber's theorem

In 1961, Gerstenhaber proved the following theorem: if k is a field and X and Y are commuting d × d matrices with entries in k, then the unital k-algebra generated by these matrices has dimension at most d. The analog of this statement for four or more commuting matrices is false. The three matrix version remains open. We use commutative–algebraic techniques to prove that the three matrix analog of Gerstenhaber's theorem is true for some new …