A universal A-infinity structure on Batalin-Vilkovisky algebras with multiple zeta value coefficients

TL;DR

This paper constructs a universal A-infinity deformation of Batalin-Vilkovisky algebras with coefficients as rational sums of multiple zeta values, revealing new algebraic structures and potential links to the Grothendieck-Teichmüller Lie algebra.

Contribution

It provides an explicit universal A-infinity deformation with coefficients expressed via multiple zeta values, extending the structure of Batalin-Vilkovisky algebras.

Findings

Deformation preserves cyclicity when starting from cyclic BV algebras.

The adjoint action of the odd Poisson bracket acts by derivations.

Potential new presentation of the Grothendieck-Teichmüller Lie algebra.

Abstract

We explicitly construct a universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky algebra that we start with is cyclic, then so is the A-infinity deformation. Moreover, the adjoint action of the odd Poisson bracket acts by derivations of the A-infinity structure. The construction conjecturally defines a new presentation of the Grothendieck-Teichmueller Lie algebra.