Modified Double Poisson Brackets

TL;DR

This paper introduces a non skew-symmetric generalization of double Poisson brackets, enabling the construction of broader H0-Poisson structures on associative algebras while retaining key properties of the original brackets.

Contribution

It presents a novel non skew-symmetric version of double Poisson brackets that extends the class of H0-Poisson structures on associative algebras.

Findings

Allows explicit construction of more general H0-Poisson structures

Retains major properties of original double Poisson brackets

Extends the theoretical framework of Poisson structures

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.