Signature maps from positive cones on algebras with involution

TL;DR

This paper develops a method to derive signatures of hermitian forms directly from positive cones on algebras with involution, improving previous results and clarifying the algebraic structure of these signatures.

Contribution

It introduces a new approach to obtain signatures from positive cones, rectifying earlier issues and enhancing understanding of hermitian form signatures on algebras with involution.

Findings

Signatures of hermitian forms can be directly derived from positive cones.

The approach rectifies previous inaccuracies in the theory.

Provides a clearer algebraic framework for signatures in this context.

Abstract

We introduced positive cones in an earlier paper as a notion of ordering on central simple algebras with involution that corresponds to signatures of hermitian forms. In the current paper we describe signatures of hermitian forms directly out of positive cones, and also use this approach to rectify a problem that affected some results in the previously mentioned paper.