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arXiv · 2006.07621

Information geometry on groupoids: the case of singular metrics

Katarzyna Grabowska·Janusz Grabowski·Marek Kus·Giuseppe Marmo
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Abstract

We use the general setting for contrast (potential) functions in statistical and information geometry provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give rise to two-forms and three-forms on the corresponding Lie algebroid. We study the case when the two-form is degenerate and show how in sufficiently regular cases one reduces it to a pseudometric structures. Transversal Levi-Civita connections for Riemannian foliations are generalized to the Lie groupoid/Lie algebroid case.

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BibTeXRIS

Katarzyna Grabowska, Janusz Grabowski, Marek Kus, Giuseppe Marmo. 2020-06-13. Information geometry on groupoids: the case of singular metrics. https://doi.org/10.1142/s1230161220500158

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