What type of study is this?

This is a Quantitative Study study.

October 12, 2025Open Access

Quartic BV structures in supercategories and modified necklace Lie bialgebras

Key Points

The modified necklace Lie bialgebra introduces bracket adjustments to arrow pairs, enhancing classical structures.
This work shows a direct connection between modified necklace operations and quartic Poisson structures on representation varieties.
Constructions utilize symmetric monoidal categories, allowing for a detailed exploration of graded differential operators.
The general categorical framework provides a basis for relating modified and classical necklace structures.

Abstract

We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side take place in symmetric monoidal Π-categories, which prompts a discussion of graded differential operators on commutative monoids in any such category. The generality of the categorical approach allows us to fully recover necklace structures, showing how the modified and classical necklace operations are related via dualisability.

Read Full Paperexternally

Ask AI

Helpful

Bookmark

View Full Paper

Cite This Study

Nikolai Perry (Tue,) studied this question.

synapsesocial.com/papers/68ec384042a190b2c351999c https://doi.org/https://doi.org/10.48550/arxiv.2509.07975