Tropical Matrix Groups

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We study the structure of groups of finitary tropical matrices under multiplication. We show that the maximal groups of n×nn×n tropical matrices are precisely the groups of the form G×RG×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.

Bibliographical metadata

Original languageEnglish
JournalSemigroup Forum
Early online date14 Sep 2017
StatePublished - 2017