群类群上的信息几何:奇异度量的情况

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Open Systems & Information Dynamics Pub Date : 2020-06-13 DOI:10.1142/s1230161220500158

K. Grabowska, J. Grabowski, M. Kuś, G. Marmo

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引用次数: 5

摘要

我们使用统计和信息几何中由李群和李代数群提供的对比(势)函数的一般设置。在李群上定义了对比函数，并在相应的李代数上得到了两种形式和三种形式。我们研究了二形式简并的情况，并展示了如何在足够规则的情况下将其简化为伪度量结构。将黎曼叶的横向Levi-Civita连接推广到李群/李代数情形。

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Information geometry on groupoids: the case of singular metrics

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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来源期刊

Open Systems & Information Dynamics 工程技术-计算机：信息系统

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Journal is to promote interdisciplinary research in mathematics, physics, engineering and life sciences centered around the issues of broadly understood information processing, storage and transmission, in both quantum and classical settings. Our special interest lies in the information-theoretic approach to phenomena dealing with dynamics and thermodynamics, control, communication, filtering, memory and cooperative behaviour, etc., in open complex systems.