Algebraic sets defined by the commutator matrix

Madi Yerlanov, Zhibek Kadyrsizova

2022

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DOI 10.1016/j.jalgebra.2021.09.012

Data confidence 70 medium

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Abstract

In this paper we study algebraic sets of pairs of matrices defined by the vanishing of either the diagonal of their commutator matrix or its anti-diagonal. We find systems of parameters for the coordinate rings of these two sets and their intersection and show that they are complete intersections. Moreover, we prove that these algebraic sets are F-pure over a field of positive prime characteristic and the algebraic set of pairs of matrices with the zero diagonal commutator is F-regular.