Lorentz Center - Order Structures, Jordan Algebras and Geometry from 29 May 2017 through 2 Jun 2017
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    Order Structures, Jordan Algebras and Geometry
    from 29 May 2017 through 2 Jun 2017

 

Description and aim

The concept of a Jordan algebra has a long and rich history in mathematics. It was originally introduced by Pascual Jordan as a way of finding alternative settings for quantum mechanics, but it turned out to have numerous connections with distinct areas of mathematics including, Lie theory, geometry, and mathematical analysis.  The finite dimensional Euclidean Jordan algebras were characterized by  Koecher and Vinberg in terms of symmetric cones. Their characterization  provides  a striking  link with Riemannian geometry of real manifolds.  For infinite dimensional real Jordan algebras no such characterization is known. Recent findings, however, indicate that in infinite dimensions there may exist  alternative characterizations of real Jordan algebras in terms of the geometry of cones and their associated order structure.

 

The main objective of this workshop is to explore the possibilities of establishing such alternative characterizations of Jordan algebras, to discuss the challenges that come with it, and to gain a deeper understanding of the geometry that is encoded in a Jordan algebra.

 

Core topics of the workshop include:

 

1. Finsler geometries on cones in order unit spaces.

2. Geometric aspects of cones in JB-algebras.

3. Cones as Banach-Finsler manifolds.

4. Order-antimorphisms on cones and Jordan structures.

5. Cones as symmetric spaces.



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