Grothendieck-Teichm\"uller and Batalin-Vilkovisky

Abstract

It is proven that, for any affine supermanifold $M$ equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ on the set of quantum BV structures (i. e.\ solutions of the quantum master equation) on $M$.