40 citations · 146 across the 22 of their papers we have counts for
22 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…
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…
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…
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…
Modified double brackets and a conjecture of S. Arthamonov
Maxime Fairon
Around 20 years ago, M. Van den Bergh introduced double Poisson brackets as operations on associative algebras inducing Poisson brackets under the representation functor. Weaker ve…
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…
Functorial constructions related to double Poisson vertex algebras
Tristan Bozec, Maxime Fairon, Anne Moreau
For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation…
Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of
M. Fairon, L. Feher
We construct a master dynamical system on a quasi-Poisson manifold, , built from the double an…
Around Van den Bergh's double brackets for different bimodule structures
Maxime Fairon, Colin McCulloch
A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an associative algebra which induces a Poisson bracket on each representation space $\operatornam…
A decoupling property of some Poisson structures on supporting Poisson-Lie symmetry
M. Fairon, L. Feher
We study a holomorphic Poisson structure defined on the linear space that is covariant under t…
Double Multiplicative Poisson Vertex Algebras
Maxime Fairon, Daniele Valeri
We develop the theory of double multiplicative Poisson vertex algebras. These structures, defined at the level of associative algebras, are shown to be such that they induce a clas…
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…
Euler continuants in noncommutative quasi-Poisson geometry
Maxime Fairon, David Fernández
It was established by Boalch that Euler continuants arise as Lie group valued moment maps for a class of wild character varieties described as moduli spaces of points on $\mathbb{P…
On the noncommutative Poisson geometry of certain wild character varieties
Maxime Fairon, David Fernández
To show that certain wild character varieties are multiplicative analogues of quiver varieties, Boalch introduced colored multiplicative quiver varieties. They form a class of (non…
Superintegrability of Calogero-Moser systems associated with the cyclic quiver
Maxime Fairon, Tamás Görbe
We study complex integrable systems on quiver varieties associated with the cyclic quiver, and prove their superintegrability by explicitly constructing first integrals. We interpr…
Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
Maxime Fairon
Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of algebras endowed with a (quasi-)Poisson bracket. In this work, we provide a study o…
Trigonometric real form of the spin RS model of Krichever and Zabrodin
M. Fairon, L. Feher, I. Marshall
We investigate the trigonometric real form of the spin Ruijsenaars-Schneider system introduced, at the level of equations of motion, by Krichever and Zabrodin in 1995. This pioneer…
Double quasi-Poisson brackets : fusion and new examples
Maxime Fairon
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 cla…
On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
Oleg Chalykh, Maxime Fairon
We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamilto…
Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
Maxime Fairon
We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with vertices. Their global Poisson structure is characterised by quasi-Hamil…
Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
Oleg Chalykh, Maxime Fairon
We study some classical integrable systems naturally associated with multiplicative quiver varieties for the (extended) cyclic quiver with vertices. The phase space of our inte…
Introduction to graded geometry
Maxime Fairon
This paper aims at setting out the basics of -graded manifolds theory. We introduce -graded manifolds from local models and give some of their properties. T…