Zinbiel algebras and multiple zeta values

Abstract

We build, using the notion of Zinbiel algebra, some commutative subalgebras $C_{u,v}$ inside an algebra of formal iterated integrals. There is a quotient map from this algebra of formal iterated integrals to the algebra of motivic multiple zeta values. Restricting this quotient map to the subalgebras $C_{u,v}$ gives a morphism of graded commutative algebras with the same graded dimension. This is conjectured to be generically an isomorphism. When $u+v=0$, the image is instead a subalgebra of the algebra of motivic multiple zeta values.