Lie solvability and the identity [x1,y1][x2,y2]⋯[xq,yq]=0 in certain matrix algebras

An in depth analysis of the maximum dimension of a subalgebra of the full n×n matrix algebra Mn(F) over a field F satisfying the identity [x1,y1][x2,y2]⋯[xq,yq]=0 (as obtained in [5]) leads to a more detailed formula for this maximum dimension, as well to a precise way of obtaining a class of examples of F-subalgebras of Mn(F) having this dimension, and finally to determining exactly when a simplified version of the mentioned formula can be used.