INFORMATION GEOMETRY FOR SOME LIE ALGEBRAS

DOI10.1142/S0219025799000254zbMath1043.81592OpenAlexW2010758375MaRDI QIDQ4810349

R. F. Streater, Hanna Nencka

Publication date: 3 September 2004

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025799000254

Mathematics Subject Classification ID

Quantum stochastic calculus (81S25) Foundations, quantum information and its processing, quantum axioms, and philosophy (81P99) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Lie algebras and Lie superalgebras (17B99)

Related Items (2)

Poisson geometry of the statistical Frobenius manifold ⋮ Souriau-Casimir Lie Groups Thermodynamics and Machine Learning

Cites Work

• Complex analytic coordinates in almost complex manifolds
• The transition probability in the state space of a \(^*\)-algebra
• Generating functions for the affine symplectic group
• A gas of Brownian particles in statistical dynamics
• \(\alpha\)-divergence of the non-commutative information geometry
• Information geometry and reduced quantum description
• Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• The Bogoliubov inner product in quantum statistics
• Spectral decomposition of the operator p2–q2
• Representations of Osp(2, 1) and the metaplectic representation
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry
• Geometry of canonical correlation on the state space of a quantum system
• The second order extension of the Gibbs state

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