The F-regularity of algebraic sets related to commutator matrices.

We study the algebraic sets of pairs of matrices defined by the vanishing of the anti-diagonal as well as the cross-diagonal of their commutator matrix. We prove that, over a field of prime characteristic, the coordinate ring of the latter is always F -regular and, with exactly one exception, so is that of the former, thus proving a conjecture of Kadyrsizova and Yerlanov. [ABSTRACT FROM AUTHOR]