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Article Dans Une Revue Forum of Mathematics, Sigma Année : 2023

Calabi-Yau structures on (quasi-)bisymplectic algebras

Résumé

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 application 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.
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Dates et versions

hal-03624186 , version 1 (24-02-2024)
hal-03624186 , version 2 (26-02-2024)

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Tristan Bozec, Damien Calaque, Sarah Scherotzke. Calabi-Yau structures on (quasi-)bisymplectic algebras. Forum of Mathematics, Sigma, 2023, 11, pp.e87. ⟨10.1017/fms.2023.88⟩. ⟨hal-03624186v2⟩
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