Double Poisson algebras
Michel Van den Bergh
Abstract
In this paper we develop Poisson geometry for non-commutative algebras. This generalizes the bi-symplectic geometry which was recently, and independently, introduced by Crawley-Boevey, Etingof and Ginzburg. Our (quasi-)Poisson brackets induce classical (quasi-)Poisson brackets on representation spaces. As an application we show that the moduli spaces of representations associated to the deformed multiplicative preprojective algebras recently introduced by Crawley-Boevey and Shaw carry a natural Poisson structure.
Create a lesson
Related papers
Galois-modular obstructions to the categorification of near-group fusion rings
Víctor Blasco
The Askey-Wilson Function is the Laplace Transform of a Positive Measure
Aaron Agulnick
Associated Varieties of Finite-Group Orbifolds
Andrew Riesen
Haagerup symmetries of the E8 theory and conformal nets at central charge eight
Cédric Arhancet
Centralizers of maps as automorphism groups of Yang--Baxter solutions
Gigel Militaru
Quaternionic and Octonionic Frameworks for Quantum Computation: Mathematical Structures, Models, and Fundamental Limitations
Johan Heriberto Rúa Muñoz, Jorge Eduardo Mahecha Gómez, Santiago Pineda Montoya