Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"
sala 2.23, ul. Pasteura 5
2024-06-19 (14:15) 
Cornelia Vizman (West University of Timisoara)
Universal extensions of Lie algebras of Hamiltonian/divergence free vector fields
Joint work with Bas Janssens (Delft University of Technology) and Leonid Ryvkin (University Claude Bernard Lyon 1)
Abstract: This talk is about two conjectures by Claude Roger in [2]. I will shortly recall our older work [1], where we prove the conjecture about the universal central extension of the Lie algebra of Hamiltonian vector fields. Then I will focus on the universal central extension of the Lie algebra of exact divergence free vector fields. To prove this second conjecture, one needs to make a detour in the realm of Leibniz algebras.
References:
[1] B. Janssens, C. Vizman, Universal central extension of the Lie algebra of Hamiltonian vector fields, IMRN, 2016.16(2016) 4996-5047.
[2] C. Roger, Extensions centrales d'algèbres et de groupes de Lie de dimension infinie, algèbre de Virasoro et généralisations, Rep. Math. Phys., 35(1995) 225–266
Abstract: This talk is about two conjectures by Claude Roger in [2]. I will shortly recall our older work [1], where we prove the conjecture about the universal central extension of the Lie algebra of Hamiltonian vector fields. Then I will focus on the universal central extension of the Lie algebra of exact divergence free vector fields. To prove this second conjecture, one needs to make a detour in the realm of Leibniz algebras.
References:
[1] B. Janssens, C. Vizman, Universal central extension of the Lie algebra of Hamiltonian vector fields, IMRN, 2016.16(2016) 4996-5047.
[2] C. Roger, Extensions centrales d'algèbres et de groupes de Lie de dimension infinie, algèbre de Virasoro et généralisations, Rep. Math. Phys., 35(1995) 225–266