Izhakian, Zur and Knebusch, Manfred (2020) Quasilinear convexity and quasilinear stars in the ray space of a supertropical quadratic form. LINEAR & MULTILINEAR ALGEBRA, 68 (12). pp. 2347-2389. ISSN 0308-1087, 1563-5139
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Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity, which is consistent with quasilinearity. A criterion for quasilinearity is specified by a Cauchy-Schwartz ratio which paves the way to a convex geometry on Ray(V), supported by a 'supertropical trigonometry'. Employing a (partial) quasiordering on Ray(V), this approach allows for producing convex quasilinear sets of rays, as well as paths, which contain a given quasilinear set in a systematic way. Minimal paths are endowed with a surprisingly rich combinatorial structure, delivered to the graph determined by pairs of quasilinear rays - apparently a fundamental object in the theory of supertropical quadratic forms.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MODULES; Tropical algebra; supertropical modules; bilinear forms; quadratic forms; quadratic pairs; ray spaces; convex sets; quasilinear sets; Cauchy-Schwarz ratio |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Mar 2021 08:03 |
| Last Modified: | 08 Mar 2021 08:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43310 |
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