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Lie groupoids in information geometry

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dc.abstract.enWe demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one 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. If the two-form is non-degenerate, it defines a ‘pseudo-Riemannian’ metric on the Lie algebroid and a family of Lie algebroid torsion-free connections, including the Levi-Civita connection of the metric. In this framework, the two-point functions are just functions on the pair groupoid M × M with the ‘standard’ metric and affine connection on the Lie algebroid TM. We study also reductions of such systems and infinite-dimensional examples. In particular, we find a contrast function defining the Fubini-Study metric on the Hilbert projective space
dc.affiliationUniwersytet Warszawski
dc.contributor.authorGrabowski, Janusz
dc.contributor.authorGrabowska, Katarzyna
dc.contributor.authorKuś, Marek
dc.contributor.authorMarmo, Giuseppe
dc.date.accessioned2024-01-25T05:09:45Z
dc.date.available2024-01-25T05:09:45Z
dc.date.issued2019
dc.description.financeNie dotyczy
dc.description.volume52
dc.identifier.doi10.1088/1751-8121/AB542E
dc.identifier.issn1751-8113
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/111201
dc.identifier.weblinkhttps://iopscience.iop.org/article/10.1088/1751-8121/ab542e/meta
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.pages505202-1-505202-22
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.encontrast functions
dc.subject.eninformation geometry
dc.subject.enLie groupoids and algebroids
dc.titleLie groupoids in information geometry
dc.typeJournalArticle
dspace.entity.typePublication