Work

Orders and polytropes: matrix algebras from valuations

Year: 2021

Type: article

Abstract: We apply tropical geometry to study matrix algebras over a field with valuation. Using the shapes of min-max convexity, known as polytropes, we revisit the graduated orders introduced by Plesken and Zassenhaus. These are classified by the polytrope region. We advance the ideal theory of graduated orders by introducing their ideal class polytropes. This article emphasizes examples and computations. It offers first steps in the geometric combinatorics of endomorphism rings of configurations in affine buildings.

Source: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

DOI: 10.1007/s13366-021-00600-4

Authors: Yassine El Maazouz, Marvin Anas Hahn, Gabriele Nebe, Mima Stanojkovski, Bernd Sturmfels

Institutions: University of California, Berkeley, Max Planck Institute for Mathematics in the Sciences, RWTH Aachen University

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,780

Funder: Deutsche Forschungsgemeinschaft