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