Multiplicative structure of 2x2 tropical matrices
Marianne Johnson, Mark Kambites
TL;DR
This paper explores the algebraic structure of 2x2 tropical matrices, providing a comprehensive description of Green's relations, idempotents, and maximal subgroups using tropical geometry techniques.
Contribution
It offers a complete characterization of the algebraic structure of the semigroup of 2x2 tropical matrices, including Green's relations and subgroup structure.
Findings
Complete description of Green's relations for 2x2 tropical matrices
Identification of all idempotent matrices in the semigroup
Characterization of maximal subgroups within the semigroup
Abstract
We study the algebraic structure of the semigroup of all tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of Green's relations and the idempotents and maximal subgroups of this semigroup.
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Taxonomy
Topicsgraph theory and CDMA systems · Polynomial and algebraic computation · Coding theory and cryptography