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Supertropical SLn

Zur Izhakian 1 Adi Niv 2 Louis Rowen 3
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetrized supertropical version SLn of the special linear group, which we partition into submonoids, based on " quasi-identity " matrices, and we display maximal sub-semigroups of SLn. We also study the monoid generated by SLn. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on SLn, which enables one to connect different matrices in SLn, but in a weaker sense than the classical situation.
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https://hal.inria.fr/hal-01253424
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Submitted on : Friday, January 22, 2016 - 10:09:57 AM
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  • HAL Id : hal-01253424, version 1
  • ARXIV : 1508.04483

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Zur Izhakian, Adi Niv, Louis Rowen. Supertropical SLn . 2015. ⟨hal-01253424⟩

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