On 14th March, Olivier Elchinger will speak in our geometry seminar. The talk will be at 1.30pm and the room will be confirmed shortly. His title is “Perturbation of formality for universal enveloping algebras” and his abstract is below.
In 1997, Kontsevich proved his formality result for symmetric algebras, implying that every Poisson manifold has a deformation quantization. We study the case of enveloping algebras of Lie algebras, for the examples of free algebras, the Lie algebra so(3), and the Heisenberg algebra. We show that for these examples, there is no formality in Kontsevich’s sense, but with a perturbation, there is a L-infinity morphism between the cohomology and the chain complex. We compute the cohomology of these algebras and proceed to the construction of said L-infinity morphism.