Generalized Reduction Procedure: Symplectic and Poisson Formalism

TL;DR

This paper introduces a unified algebraic reduction procedure applicable to symplectic and Poisson structures, extending traditional methods and including a non-commutative example.

Contribution

It presents a generalized reduction framework that unifies existing methods and extends to non-commutative settings using an algebraic approach.

Findings

Unified reduction procedure encompassing existing methods

Application to non-commutative geometry

Simplified algebraic framework for reduction

Abstract

We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non-commutative setting.