# Double quasi-Poisson brackets : fusion and new examples

## TL;DR

This paper introduces new examples of double quasi-Poisson brackets using fusion, extending Van den Bergh's method to all such brackets and providing alternative constructions for those related to quivers and surface groups.

## Contribution

It extends the fusion method to arbitrary double quasi-Poisson brackets and offers new constructions for brackets associated with quivers and surface fundamental groups.

## Key findings

- Extended fusion method to all double quasi-Poisson brackets
- Provided new examples based on classification and fusion
- Alternative construction for brackets related to quivers and surfaces

## Abstract

We exhibit new examples of double quasi-Poisson brackets, based on some classification results and the method of fusion. This method was introduced by Van den Bergh for a large class of double quasi-Poisson brackets which are said differential, and our main result is that it can be extended to arbitrary double quasi-Poisson brackets. We also provide an alternative construction for the double quasi-Poisson brackets of Van den Bergh associated to quivers, and of Massuyeau-Turaev associated to the fundamental groups of surfaces.