
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.
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