Homogeneous statistical manifolds
Differential Geometry
2024-08-06 v1 Mathematical Physics
math.MP
Abstract
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of homogeneous statistical manifolds. In particular we construct explicit examples of homogeneous statistical manifolds of low dimension. The second purpose is to classify -dimensional Lie groups admitting non-trivial conjugate symmetric left invariant statistical structure.
Cite
@article{arxiv.2408.01647,
title = {Homogeneous statistical manifolds},
author = {Jun-ichi Inoguchi and Yu Ohno},
journal= {arXiv preprint arXiv:2408.01647},
year = {2024}
}