28 citations · 85 across the 17 of their papers we have counts for
19 papers
A Knebusch trace formula for Azumaya algebras with involution
Vincent Astier, Thomas Unger
We establish a trace formula for signatures of hermitian forms over Azumaya algebras with involution, extending Knebusch's work on symmetric bilinear forms over finite étale extens…
Continuity of total signature maps for Azumaya algebras with involution
Vincent Astier, Thomas Unger
In this paper we continue our investigation of signatures of hermitian forms over Azumaya algebras with involution over commutative rings. We show that the approach used in an earl…
Signature maps from positive cones on algebras with involution
Vincent Astier, Thomas Unger
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 curren…
Pfister's local-global principle for Azumaya algebras with involution
Vincent Astier, Thomas Unger
We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular…
Trichotomy for positive cones and a maximality counterexample
Vincent Astier, Thomas Unger
In [4] we developed the theory of positive cones on finite-dimensional simple algebras with involution, inspired by the classical Artin-Schreier theory of orderings on fields, and…
Galois extensions, positive involutions and an application to unitary space-time coding
Vincent Astier, Thomas Unger
We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution will be a Galois extension of the fixe…
Positive cones and gauges on algebras with involution
Vincent Astier, Thomas Unger
We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We als…
Hermitian Morita Theory: a Matrix Approach
David W. Lewis, Thomas Unger
This bundle contains the paper "Hermitian Morita Theory: a Matrix Approach", published in Irish Math. Soc. Bulletin 62 (2008), pp. 37-41 (reproduced with permission of the Irish Ma…
Signatures, sums of hermitian squares and positive cones on algebras with involution
Vincent Astier, Thomas Unger
We provide a coherent picture of our efforts thus far in extending real algebra and its links to the theory of quadratic forms over ordered fields in the noncommutative direction,…
Positive cones on algebras with involution
Vincent Astier, Thomas Unger
We introduce positive cones on algebras with involution. These allow us to prove analogues of Artin's solution to Hilbert's 17th problem, the Artin-Schreier theorem characterizing…
Signatures of hermitian forms, positivity, and an answer to a question of Procesi and Schacher
Vincent Astier, Thomas Unger
Using the theory of signatures of hermitian forms over algebras with involution, developed by us in earlier work, we introduce a notion of positivity for symmetric elements and pro…
Stability index for algebras with involution
Vincent Astier, Thomas Unger
In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in pa…
Signatures of hermitian forms and "prime ideals" of Witt groups
Vincent Astier, Thomas Unger
In this paper a further study is made of -signatures of hermitian forms, introduced previously by the authors. It is shown that a tuple of reference forms may be replaced by…
Weakly Hyperbolic Involutions
Karim Johannes Becher, Thomas Unger
Pfister's Local-Global Principle states that a quadratic form over a (formally) real field is weakly hyperbolic (i.e. represents a torsion element in the Witt ring) if and only if…
Space-time block codes from nonassociative division algebras
Susanne Pumpluen, Thomas Unger
Associative division algebras are a rich source of fully diverse space-time block codes (STBCs). In this paper the systematic construction of fully diverse STBCs from nonassociativ…
Signatures of hermitian forms and the Knebusch Trace Formula
Vincent Astier, Thomas Unger
Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguitie…
The Procesi-Schacher conjecture and Hilbert's 17th problem for algebras with involution
Igor Klep, Thomas Unger
In 1976 Procesi and Schacher developed an Artin-Schreier type theory for central simple algebras with involution and conjectured that in such an algebra a totally positive element…
Quadratic Forms and Space-Time Block Codes from Generalized Quaternion and Biquaternion Algebras
Thomas Unger, Nadya Markin
In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary b…
A hermitian analogue of the Broecker-Prestel theorem
Vincent Astier, Thomas Unger
The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy…