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Jean-Louis Koszul and the Elementary Structures of Information Geometry

  • Frédéric BarbarescoEmail author
Chapter
Part of the Signals and Communication Technology book series (SCT)

Abstract

This paper is a scientific exegesis and admiration of Jean-Louis Koszul’s works on homogeneous bounded domains that have appeared over time as elementary structures of Information Geometry. Koszul has introduced fundamental tools to characterize the geometry of sharp convex cones, as Koszul-Vinberg characteristic Function, Koszul Forms, and affine representation of Lie Algebra and Lie Group. The 2nd Koszul form is an extension of classical Fisher metric. Koszul theory of hessian structures and Koszul forms could be considered as main foundation and pillars of Information Geometry.

Keywords

Koszul-Vinberg characteristic function Koszul forms Affine representation of lie algebra and lie group Homogeneous bounded domains 

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Thales Land & Air Systems, Voie Pierre-Gilles de GennesLimoursFrance

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