A counterexample for Gerstenhaber's Problem concerning three commuting matrices
Patrick Teller · HAL (Le Centre pour la Communication Scientifique Directe) · 2025
Gerstenhaber's Problem concerns a commutative algebra generated by three commuting matrices in Mn(C); it is well known that in case of one or twoo matrices the dimension of the algebra is less or equal to n; on the other side, in case of k matrices (where k >2) the dimension can exced n.The case of three matrices remained open since Gerstenhaber's paper (1961).Here is a counter-example: in case of three matrices the dimension may exced n.