The moduli spaces of left-invariant statistical structures on Lie groups
Abstract
Abstract In the context of information geometry, the concept known as left-invariant statistical structure on Lie groups is defined by Furuhata–Inoguchi–Kobayashi (Inf Geom 4(1):177–188, 2021). In this paper, we introduce the notion of the moduli space of left-invariant statistical structures on a Lie group. We study the moduli spaces for three particular Lie groups, each of which has a moduli space of left-invariant Riemannian metrics that is a singleton. As applications, we classify left-invariant conjugate symmetric statistical structures and left-invariant dually flat structures (which are equivalent to left-invariant Hessian structures) on these three Lie groups. A characterization of the Amari–Chentsov $$\alpha $$ α -connections on the Takano Gaussian space is also given.
Fields of Study & Subjects
Statistical Mechanics and Entropy
Topological and Geometric Data Analysis
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Information Geometry
- Publisher
- Springer Science and Business Media LLC
- Volume
- 9
- Issue
- 1
- Pages
- 235–278
- Publication date
- 13 April 2026
- Language
- EN