Algebraic sets defined by the commutator matrix

Zhibek Kadyrsizova, Madi Yerlanov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)29-50
Number of pages22
JournalJournal of Algebra
Volume589
DOIs
Publication statusPublished - Jan 1 2022

Keywords

  • Commutator matrix
  • Complete intersection
  • F-pure
  • F-regular
  • System of parameters

ASJC Scopus subject areas

  • Algebra and Number Theory

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