The properad of quadratic Poisson structures is Koszul

TL;DR

This paper establishes a sufficient condition for properadic envelopes of quadratic dioperads to be Koszul and demonstrates that the properad of quadratic Poisson structures satisfies this condition, proving it is Koszul.

Contribution

It introduces a new criterion for Koszulness of properadic envelopes and applies it to quadratic Poisson structures, providing a novel example.

Findings

Properadic envelope of quadratic dioperads can be Koszul under certain conditions.

The properad of quadratic Poisson structures is proven to be Koszul.

Provides a new example of Koszul properad in algebraic geometry.

Abstract

In this paper, we suggest a sufficient condition on the properadic envelope of a quadratic dioperad to be Koszul in terms of twisted associative algebras. As a particular new example, we show that the properad of quadratic Poisson structures is Koszul.