Supertropical $\operatorname{SL}_n$
Zur Izhakian, Adi Niv, Louis Rowen

TL;DR
This paper develops a symmetric supertropical version of the special linear group, partitioning it into submonoids, analyzing its structure, and exploring the action of elementary matrices, revealing novel behaviors in supertropical algebra.
Contribution
It introduces a supertropical $ ext{SL}_n$ version, partitions it into submonoids, and studies its structure and matrix actions, extending supertropical algebra theory.
Findings
Partition into submonoids based on quasi-identity matrices
Identification of maximal sub-semigroups of $ ext{SLS}_n$
Illustration of unexpected behaviors in supertropical matrix actions
Abstract
Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version of the special linear group, which we partition into submonoids, based on "quasi-identity" matrices, and we display maximal sub-semigroups of . We also study the monoid generated by . 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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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology
