Higher Lie theory
December 9–11, 2013, University of Luxembourg
Supported by:
University of Luxembourg
Mathematics Research Unit
Schedule
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The lecture rooms are as follows:
| Monday 9 | Tuesday 10 | Wednesday 11 | |
|---|---|---|---|
| morning | B13 | PF | PF |
| afternoon | PF | C02 | A02 |
PF: room Paul Feidert
see the campus map to locate the rooms; on Monday morning, there will be signs to B13 from the main hall and from the math building.
Mini-course
Friedrich Wagemann,
Integration of Leibniz algebras (lecture notes)
Some methods have been developed recently to investigate smooth objects (Lie racks) which have a natural Leibniz algebra structure on their tangent spaces, and to integrate a given Leibniz algebra into such a Lie rack.
We will present preliminary material due to Kinyon and Weinstein, and then the four methods we know of to integrate Leibniz algebras.
The first known method was developed by S. Covez in his 2010 thesis.
Covez regards a Leibniz algebra as an abelian extension of a Lie algebra by some representation, and the main point is to integrate the Leibniz 2-cocycle associated to this extension.
Simon will explain the details in his lecture.
Kinyon and Kinyon–Weinstein developed two integration procedures closer to the BCH formula for Lie algebras.
Both are based on the formula X*Y = exp(adX)(Y).
A fourth procedure is developed by Mostovoy in terms of formal “group” laws.
The last part of our lectures concerns recent work by Dherin–Wagemann, where the Kinyon–Weinstein procedure
is used to deformation quantize the dual of a Leibniz algebra.
In this context, we state the quantization problem for generalized Poisson manifolds, i.e. manifolds with a non necessarily skew-symmetric Poisson bracket.
Talks
See the pdf file of the abstracts.
- Camilo Arias Abad, Higher dimensional analogues of braid representations
- Simon Covez, On the conjectural Leibniz (co)homology for groups
- Michał Jóźwikowski, Higher Lie algebroids
- Yvette Kosmann-Schwarzbach, Double Poisson brackets. A survey
- Olga Kravchenko, Knot invariants and cluster algebras
- Chris Rogers, L∞-algebras and geometric prequantization
- Dmitry Roytenberg, A Dold–Kan-type correspondence for superalgebras of differentiable functions and a “differential graded” approach to derived differential geometry
- Christopher Schommer-Pries, String connections and torsion
- Pavol Ševera, Moduli spaces of flat connections and quantizations of Lie bialgebras
- Zoran Škoda, Toward integration of Lie algebras in Loday–Pirashvili category
- Thomas Strobl, Mathematics around Lie 2-algebroids and the tensor hierarchy in gauged supergravity
- Marco Zambon, Singular foliations and subalgebroids
- Chenchang Zhu, Integration of Courant algebroids