Signature maps from positive cones on algebras with involution

2025/05/28 by Astier, Vincent, Unger, Thomas · 2 citations
#06F25 #11E39 #13J30 #16K20 #16W10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.22178

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.

Citations

• Pfister's local-global principle for Azumaya algebras with involution
• Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
• Quaternions and matrices of quaternions

Cited by

• Continuity of total signature maps for Azumaya algebras with involution
• Maximal prepositive cones on quaternion algebras with involution

Related

• Stability index for algebras with involution
• Trichotomy for positive cones and a maximality counterexample
• Continuity of total signature maps for Azumaya algebras with involution
• Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
• An Artin-Schreier-type theory for signatures of hermitian forms over involutions