Classical BV formalism for group actions

Abstract

We study the derived critical locus of a function [Formula: see text] on the quotient stack of a smooth affine scheme [Formula: see text] by the action of a smooth affine group scheme G. It is shown that [Formula: see text] is a derived quotient stack for a derived affine scheme Z, whose dg-algebra of functions is described explicitly. Our results generalize the classical BV formalism in finite dimensions from Lie algebra to group actions.