Graded geometry and generalized reduction
Symplectic Geometry
2023-09-19 v2 High Energy Physics - Theory
Differential Geometry
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.
Cite
@article{arxiv.2306.01508,
title = {Graded geometry and generalized reduction},
author = {Henrique Bursztyn and Alberto S. Cattaneo and Rajan Amit Mehta and Marco Zambon},
journal= {arXiv preprint arXiv:2306.01508},
year = {2023}
}
Comments
80 pages. v2: Added Lemma 7.1. Added Example 6.15 and consequences thereof (Examples 7.6, 7.7, 7.12, 8.20, 8.21, 8.22)