Abstract
Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a connective structure on the lifting gerbe associated to this problem. Our main result classifies all connections on the central extension of a given principal bundle. In particular, we find that admissible connections are in one-to-one correspondence with parallel trivializations of the lifting gerbe. Moreover, we prove a vanishing result for Neeb’s obstruction classes for finite dimensional Lie groups.
Original language | English |
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Title of host publication | Geometry at the Frontier |
Subtitle of host publication | Symmetries and Moduli Spaces of Algebraic Varieties |
Editors | Paola Comparin, Eduardo Esteves, Sebastián Reyes-Carocca, Rubí E. Rodríguez, Herbert Lange |
Publisher | American Mathematical Society |
Pages | 39-56 |
Volume | 766 |
ISBN (Electronic) | 978-1-4704-6422-6 |
ISBN (Print) | 978-1-4704-5327-5 |
DOIs | |
Publication status | Published - 30 Jul 2021 |
Event | Geometry at the Frontier III - Universidad de La Frontera, Pucón, Chile Duration: 12 Nov 2018 → 16 Nov 2018 |
Publication series
Name | Contemporary Mathematics |
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Publisher | American Mathematical Society |
ISSN (Print) | 0271-4132 |
ISSN (Electronic) | 1098-3627 |
Conference
Conference | Geometry at the Frontier III |
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Country/Territory | Chile |
City | Pucón |
Period | 12/11/18 → 16/11/18 |
Bibliographical note
The first author is partially supported by a J. C. Bose Fellowship.The second author thanks the TIFR, Mumbai, for hospitality during 03/2017 and was partially funded by DFG grant UP 85/2-1 of the priority program SPP 2026 Geometry at Infinity.
Keywords
- connections
- gerbes
- central extensions