Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Ciaglia, Florio M., Jost, Jürgen, Schwachhöfer, Lorenz J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212006
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction. Florio M. Ciaglia, Jürgen Jost and Lorenz J. Schwachhöfer. SIGMA 19 (2023), 078, 27 pages

Jordan algebras naturally arise in (quantum) information geometry, and we aim to understand their role and structure within this framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide a similar construction in the case of real Jordan algebras. G...