Supertropical ${\mathrm{SL}}_n$

Abstract

Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version ${\mathrm{SLS}}_n$ of the special linear group, which we partition into submonoids, based on "quasi-identity" matrices, and we display maximal sub-semigroups of ${\mathrm{SLS}}_n$. We also study the monoid generated by ${\mathrm{SLS}}_n$. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on ${\mathrm{SLS}}_n$, which enables one to connect different matrices in ${\mathrm{SLS}}_n$, but in a weaker sense than the classical situation.

One extra result added, concerning generation by elementary matrices, and some misprints corrected

References in corpus (1)

• Tropical totally positive matrices

Cited by in corpus (1)

• Modules and Lie Semialgebras over Semirings with a Negation Map