- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Lie groupoids which give rise to G-structures
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Lie groupoids which give rise to G-structures Struchiner, Ivan
Description
The infinitesimal data attached to a (“finite type” class of) G-structures with connections are its structure equations. Such structure equations give rise to Lie algebroids endowed with extra geometric information following from the fact that they come from G-structures. For example, the Lie algebroid is trivial as a vector bundle, its bracket encodes the Lie bracket and the natural representation on $R^n$ of the Lie algebra of the structure group G of the G-structure, the Lie algebroid comes equipped an action of G by inner Lie algebroid automorphisms, etc… Conversely, given a Lie algebroid as above (called a G-algebroid), a natural question is that of finding G-structures which correspond via differentiation to the Lie algebroid. This integration problem is known as “Cartan’s Realization Problem for G-Structures”. In this talk I will show that if a G-algebroid is integrable by a Lie groupoid endowed with an action of G, then each s-fiber of the groupoid can be identified with the total space of a G-structure with connection solving the realization problem. If time permits I will also explain the obstructions for finding such “G-integrations” of G-algebroids. The talk will be based on joint work with prof. Rui Loja Fernandes
Item Metadata
Title |
Lie groupoids which give rise to G-structures
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2017-04-18T15:33
|
Description |
The infinitesimal data attached to a (“finite type” class of) G-structures with connections are its structure equations. Such structure equations give rise to Lie algebroids endowed with extra geometric information following from the fact that they come from G-structures. For example, the Lie algebroid is trivial as a vector bundle, its bracket encodes the Lie bracket and the natural representation on $R^n$ of the Lie algebra of the structure group G of the G-structure, the Lie algebroid comes equipped an action of G by inner Lie algebroid automorphisms, etc…
Conversely, given a Lie algebroid as above (called a G-algebroid), a natural question is that of finding G-structures which correspond via differentiation to the Lie algebroid. This integration problem is known as “Cartan’s Realization Problem for G-Structures”. In this talk I will show that if a G-algebroid is integrable by a Lie groupoid endowed with an action of G, then each s-fiber of the groupoid can be identified with the total space of a G-structure with connection solving the realization problem. If time permits I will also explain the obstructions for finding such “G-integrations” of G-algebroids.
The talk will be based on joint work with prof. Rui Loja Fernandes
|
Extent |
44 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: University of Sao Paulo
|
Series | |
Date Available |
2017-10-16
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0357059
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International