Dirac reduction for Poisson vertex algebras

TL;DR

This paper introduces a Dirac reduction method for non-local Poisson vertex algebras, enabling the reduction of complex Poisson structures, and demonstrates its application to a generalized Drinfeld-Sokolov hierarchy.

Contribution

It develops a novel Dirac reduction framework for non-local Poisson vertex algebras, extending classical reduction techniques to a broader algebraic setting.

Findings

Successfully constructs Dirac reduction for non-local Poisson brackets.

Applies the method to a generalized Drinfeld-Sokolov hierarchy.

Provides a new tool for analyzing complex integrable systems.

Abstract

We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We apply this construction to an example of a generalized Drinfeld-Sokolov hierarchy.