Tropical matrix groups

Zur Izhakian, Marianne Johnson, Mark Kambites

Research output: Contribution to journalArticlepeer-review


We study the structure of groups of finitary tropical matrices under multiplication. We show that the maximal groups of n× n tropical matrices are precisely the groups of the form G× R where G is a group admitting a 2-closed permutation representation on n points. Each such maximal group is also naturally isomorphic to the full linear automorphism group of a related tropical polytope. Our results have numerous corollaries, including the fact that every automorphism of a projective (as a module) tropical polytope of full rank extends to an automorphism of the containing space.

Original languageEnglish
Pages (from-to)178-196
Number of pages19
JournalSemigroup Forum
Issue number1
StatePublished - 1 Feb 2018
Externally publishedYes


  • Automorphism group
  • Green’s relations
  • Semigroups
  • Tropical matrices
  • Tropical polytopes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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