The BRST Complex of Homological Poisson Reduction

Abstract

So-called BRST complexes associated to a coisotropic ideal \(J\) of a Poission algebra P provide a description of the Poisson algebr \((P/J)^J\) as their cohomology in degree zero. Using the notion of stable equivalence introduced by Felder and Kazhdan, we prove that any two BRST complexes associated to the same coisotropic ideal are quasi-isomorphic in the symplectic case \(P = \mathbb{R}[x_i,y_j]\) with \([x_i,y_j]=\delta_{ij}\). As a corollary, the cohomology of the BRST complexes is canonically associated to the coisotropic ideal \(J\) in the symplectic case. We do not require any regularity assumptions on the constraints generating the ideal \(J\).