Supertropical SLn

Zur Izhakian, Adi Niv*, Louis Rowen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number7
Early online date16 Aug 2017
Publication statusPublished - 2018

Bibliographical note

The research of the first author has been supported by the Research Councils UK (EPSRC) [grant number EP/N02995X/1]. The second author has been supported by the French Chateaubriand grant and INRIA postdoctoral fellowship.


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


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