Maximal prepositive cones on quaternion algebras with involution

TL;DR

This paper characterizes prepositive cones on quaternion algebras with involution, showing that under broad conditions, all such cones are maximal, thus advancing understanding of algebraic orderings.

Contribution

It provides a detailed description of prepositive cones in quaternion algebras with involution and proves their maximality in many cases, extending prior theoretical frameworks.

Findings

All prepositive cones are maximal in a broad class of quaternion algebras with involution.

The work advances the theoretical understanding of orderings on algebras with involution.

Provides a comprehensive description of prepositive cones in the specific algebraic context.

Abstract

We give a description of prepositive cones -- a notion of ordering on algebras with involution introduced by Astier and Unger -- in the specific context of quaternion algebras with involution. Our main result establishes that, for a broad class of quaternion algebras with involution, every prepositive cone is maximal.