Quadratic Duality for Chiral Algebras

TL;DR

This paper introduces a quadratic duality concept for chiral algebras, paralleling classical associative algebra duality, and explores its relation to Maurer-Cartan equations with explicit examples.

Contribution

It develops a novel quadratic duality framework for chiral algebras and connects it to Maurer-Cartan equations, expanding the theoretical understanding of chiral algebra structures.

Findings

Established a chiral quadratic duality concept

Linked duality to Maurer-Cartan equations in chiral algebras

Provided explicit examples illustrating the duality

Abstract

We introduce a notion of quadratic duality for chiral algebras. This can be viewed as a chiral version of the usual quadratic duality for quadratic associative algebras. We study the relationship between this duality notion and the Maurer-Cartan equations for chiral algebras, which turns out to be parallel to the associative algebra case. We also present some explicit examples.