Modified Double Poisson Brackets

Abstract

We propose a non skew-symmetric generalization of the original definition of double Poisson Bracket by M. Van den Bergh. It allows one to explicitly construct more general class of H0-Poisson structures on finitely generated associative algebras. We show that modified double Poisson brackets inherit certain major properties of the double Poisson brackets.

Appendix with an application to Integrable Systems was added

References in corpus (2)

• On double Poisson structures on commutative algebras
• Poisson-Nijenhuis structures on quiver path algebras

Cited by in corpus (4)

• Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
• Around Van den Bergh's double brackets for different bimodule structures
• Nonabelian elliptic Poisson structures on projective spaces
• Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology