Modified necklace Lie bialgebras & quartic BV structures in supercategories (Nikolai PERRY, UniGE)

09.12.2025 15:00 – 17:00

We introduce modified versions of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. These structures are related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side will take place in any suitable symmetric monoidal category, the generality of which allows us to fully recover necklace structures, giving them a new conceptual origin and revealing how the modified and classical necklace operations are related via dualisability. A broader aim of this talk is to highlight the following: (1) naïve generalisations can be fruitful, and (2) notation should be taken seriously. Time permitting, we will conclude with a few open questions.
Based on recent work arXiv:2509.07975 [math.QA].

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre