Homological reduction of Courant algebroids

Abstract

We develop a homological model for hamiltonian reduction of Courant algebroids, parallel to the BFV formulation of hamiltonian reduction in symplectic geometry. To a hamiltonian action on a Courant algebroid, we associate a differential graded Courant--Dorfman algebra, obtained from the BFV algebra of the corresponding graded symplectic manifold; under usual regularity assumptions, its cohomology recovers the Courant--Dorfman algebra of the reduced Courant algebroid.