Calabi-Yau structures on (quasi-)bisymplectic algebras [article]

Tristan Bozec, Damien Calaque, Sarah Scherotzke
2022 arXiv   pre-print
We show that relative Calabi--Yau structures on noncommutative moment maps give rise to (quasi-)bisymplectic structures, as introduced by Crawley-Boevey-Etingof-Ginzburg (in the additive case) and Van den Bergh (in the multiplicative case). We prove along the way that the fusion process (a) corresponds to the composition of Calabi-Yau cospans with "pair-of-pants" ones, and (b) preserves the duality between non-degenerate double quasi-Poisson structures and quasi-bisymplectic structures. As an
more » ... plication we obtain that Van den Bergh's Poisson structures on the moduli spaces of representations of deformed multiplicative preprojective algebras coincide with the ones induced by the 2-Calabi-Yau structures on (dg-versions of) these algebras.
arXiv:2203.14382v1 fatcat:7jxflnshknfnznheyzhqdpbd6q