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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids

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Author(s):
Kotov, Alexei [1] ; Strobl, Thomas [2, 3]
Total Authors: 2
Affiliation:
[1] Univ Hradec Kralove, Fac Sci, Rokitanskeho 62, Hradec Kralove 50003 - Czech Republic
[2] UMI CNRS 2924, IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro - Brazil
[3] Univ Claude Bernard Lyon 1, Univ Lyon, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne - France
Total Affiliations: 3
Document type: Journal article
Source: LETTERS IN MATHEMATICAL PHYSICS; v. 108, n. 3, SI, p. 737-756, MAR 2018.
Web of Science Citations: 2
Abstract

Cartan-Lie algebroids, i.e., Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids with ad-invariant (Riemannian) metrics on their fibers and base and g, respectively. We determine the necessary and sufficient conditions for a positive quadratic Lie algebroid to integrate to a Riemannian Cartan-Lie groupoid. Here we mean a Cartan-Lie groupoid equipped with a bi-invariant and inversion-invariant metric on such that it induces by submersion the metric g on its base and its restriction to the t-fibers coincides with . (AU)

FAPESP's process: 11/11973-4 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics
Grantee:Nathan Jacob Berkovits
Support type: Research Projects - Thematic Grants