Martin Markl: Combinatorics of multilinear differential operators, or still another explanation of the ubiquity of Lie and strongly homotopy Lie algebras

Abstract: As a motivation, we start with analysis of the interplay between the classical Jacobi identity and differential operators, and compare it with the effect of the associator. Moving to the ‘quantized’ level, we compare the nature of the big bracket and IBL(=infinitesimal Lie bialgebras)-infinity algebras with Terilla's quantization of associative algebras. In the second part, we introduce a filtration mimicking combinatorial properties of multidifferential operators, and the associated notion of tight operads. We then come back to Lie algebras and give another reason why they deserve to be, along with commutative and associative algebras, recognized as one of the Three Graces. The talk will be based on the paper “Calculus of multilinear differential operators, operator \(L_\infty\)-algebras and \({\it IBL}_\infty\)-algebras” of Denis Bashkirov and mine. Its preprint is available at https://arxiv.org/abs/2108.12158, published version at https://users.math.cas.cz/~markl/.