Orders and Polytropes: Matrix Algebras from Valuations
Combinatorics
2021-11-23 v2 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2107.00503,
title = {Orders and Polytropes: Matrix Algebras from Valuations},
author = {Yassine El Maazouz and Marvin Anas Hahn and Gabriele Nebe and Mima Stanojkovski and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2107.00503},
year = {2021}
}
Comments
14 pages