Oberseminar Deformationsquantisierung und Geometrie: ``A-infinity algebras arising from Lie pairs'' by Mathieu Stiénon (Penn State University)

Abstract: Given an inclusion A → L of Lie algebroids sharing the same base manifold $M$, i.e. a Lie pair, the graded vector space Γ(Λ•A∗) ⊗C∞(M ) D, admits a natural but non-obvious $A_\infty$ algebra structure --- $D$ denotes the quotient of the universal enveloping algebra of the Lie algebroid $L$ by the left ideal generated by $\Gamma(A)$. I will explain how this $A_\infty$ algebra structure is inherited, by homotopy transfer, from the universal enveloping algebra of the differential graded Lie algebroid arising as the pullback of the Lie algebroid $L\to M$ through the canonical surjective submersion $A[1]\to M$. This is a joint work with Luca Vitagliano and Ping Xu.

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