9 papers
Double Transposed Poisson Algebras
Maxime Fairon, Nikita Safonkin
We introduce double transposed Poisson algebras, a noncommutative analogue of the transposed Poisson algebras of Bai, Bai, Guo and Wu that is compatible with the Kontsevich--Rosenb…
Double Poisson (vertex) algebra cohomology
Maxime Fairon, Daniele Valeri
A noncommutative (NC) version of Poisson geometry was initiated by Van den Bergh by introducing at the level of associative algebras the formalism of double Poisson brackets. Their…
Quasi-Poisson varieties from double quasi-Poisson algebras in types
Semeon Arthamonov, Maxime Fairon
Double (quasi-)Poisson brackets were introduced on associative algebras by Van den Bergh to induce a (quasi-)Poisson structure on their representation spaces naturally equipped wit…
Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
L. Feher, M. Fairon
We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group on a manifold descends to an integrable system on a dense open su…
Compatible Poisson structures on multiplicative quiver varieties
Maxime Fairon
Any multiplicative quiver variety is endowed with a Poisson structure constructed by Van den Bergh through reduction from a Hamiltonian quasi-Poisson structure. The smooth locus ca…
Integrable systems on multiplicative quiver varieties from cyclic quivers
Maxime Fairon
We consider a class of complex manifolds constructed as multiplicative quiver varieties associated with a cyclic quiver extended by an arbitrary number of arrows starting at a new…