Supertropical SLn

Zur Izhakian, Adi Niv*, Louis Rowen

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.

Original languageEnglish
Pages (from-to)1461-1483
Number of pages23
JournalLinear and Multilinear Algebra
Volume66
Issue number7
Early online date16 Aug 2017
DOIs
Publication statusPublished - 2018

Keywords

  • elementary matrix
  • matrix monoid
  • quasi-identity
  • special linear monoid
  • Supertropical matrix algebra
  • tropical adjoint matrix

ASJC Scopus subject areas

  • Algebra and Number Theory

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