Identities of tropical matrix semigroups and the plactic monoid of rank 4

Thomas Aird

Research output: Contribution to journalArticlepeer-review

Abstract

We study semigroup varieties generated by full and upper triangular tropical matrix semigroups and the plactic monoid of rank 4. We prove that the upper triangular tropical matrix semigroup UTn(T) generates a different semigroup variety for each dimension n. We show a weaker version of this fact for the full matrix semigroup: full tropical matrix semigroups of different prime dimensions generate different semigroup varieties. For the plactic monoid of rank 4, P4, we find a new set of identities satisfied by P4 shorter than those previously known, and show that the semigroup variety generated by P4 is strictly contained in the variety generated by UT5(T).
Original languageEnglish
Article number10.1142/S0218196722500461
Pages (from-to)1083 - 1100
Number of pages18
JournalInternational Journal of Algebra and Computation
Volume32
Issue number6
DOIs
Publication statusPublished - 21 May 2022

Keywords

  • Identities
  • Varieties
  • Tropical Matrices
  • Plactic Monoids
  • Upper Triangular Matrix Semigroups

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