Graded geometry and generalized reduction

TL;DR

This paper develops a unified framework for reducing Courant, Dirac, and generalized complex structures using graded symplectic geometry, providing systematic methods that encompass existing reduction schemes.

Contribution

It introduces a graded symplectic reduction approach for generalized structures, unifying and extending previous reduction methods in the field.

Findings

Systematic reduction procedures for Courant, Dirac, and generalized complex structures.

Recovery of known reduction schemes as special cases.

Framework applicable in both coisotropic and hamiltonian settings.

Abstract

We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out graded symplectic reduction, both in the coisotropic and hamiltonian settings. Specializing the latter to the exact case, we recover in a systematic way the reduction schemes of Bursztyn-Cavalcanti-Gualtieri.