Kapranov L-infinity algebras
Time: 2026-05-06
Published By: Ruixin Li
Speaker(s): Ping Xu (University of Auckland)
Time: 14:00-15:00 May 26, 2026
Venue: Room 29, Quan Zhai, BICMR
Abstract: In his study of Rozansky–Witten invariants, Kapranov discovered a natural $L_\infty[1]$-algebra structure on the Dolbeault complex $\Omega^{0, \bullet}(T_X^{1, 0})$ of an arbitrary Kähler manifold $X$, where all multibrackets are $\Omega^{0, \bullet}(X)$-multilinear except for the unary bracket. Motivated by this example, we introduce an abstract notion of Kapranov L-infinity algebras, and prove that associated to any dg Lie algebroid, there is a natural Kapranov L-infinity algebra. We also discuss the linearization problem. This is a joint work with Ruggero Bandiera, Seokbong Seol, and Mathieu Stiénon.
