Zinbiel algebras and multiple zeta values

Abstract

We build, using the notion of zinbiel algebra, some commutative sub-algebras 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 sub-algebras 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 sub-algebra of the algebra of motivic multiple zeta values.

Demi-shuffle duals of Magnus polynomials in a free associative algebra

“…Note 4.6. A noteworthy notion closely related to our S (k) , S (k,λ) is the free Zinbiel (or, dual Leibniz) algebra studied by J.-L. Loday [8], I. Dokas [2], F. Chapoton [1] and others. Let V be a vector space with a basis B = {X 0 , X 1 , .…”