Multiplicative connections and their Lie theory
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Published:2021-10-25
Issue:
Volume:
Page:
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ISSN:0219-1997
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Container-title:Communications in Contemporary Mathematics
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language:en
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Short-container-title:Commun. Contemp. Math.
Author:
Pugliese Fabrizio1,
Sparano Giovanni1,
Vitagliano Luca1
Affiliation:
1. DipMat, Università degli Studi di Salerno, via Giovanni Paolo II, 123, 84084 Fisciano (SA), Italy
Abstract
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the sense that a linear connection on a Lie groupoid is multiplicative if and only if its torsion is a multiplicative tensor in the sense of Bursztyn–Drummond [Lie theory of multiplicative tensors, Mat. Ann. 375 (2019) 1489–1554, arXiv:1705.08579] and its geodesic spray is a multiplicative vector field. We identify the obstruction to the existence of a multiplicative connection. We also discuss the infinitesimal version of multiplicative connections in the tangent bundle, that we call infinitesimally multiplicative (IM) connections and we prove an integration theorem for IM connections. Finally, we present a few toy examples.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,General Mathematics
Cited by
1 articles.
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