Real Algebraic and Analytic Geometry

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357. Vincent Astier and Thomas Unger:
Positive cones on algebras with involution.

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Submission: 2016, September 27.

We introduce positive cones on algebras with involution. These allow us to prove analogues of Artin's solution to Hilbert's 17th problem and the Artin-Schreier theorem characterizing formally real fields. We introduce the corresponding space of orderings of an algebra with involution and investigate its topological properties, showing in particular that it is a spectral space. As an application we solve the problem of the existence of positive involutions. .

Mathematics Subject Classification (2010): 13J30, 16K20, 11E39.

Full text, 40p.: pdf 246k.

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