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arXiv · 2109.00241

Zinbiel algebras and multiple zeta values

Frédéric Chapoton
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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 $C_{u,v}$ of A$_{1,0}$ 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.

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Frédéric Chapoton. 2021-09-01. Zinbiel algebras and multiple zeta values. https://arxiv.org/abs/2109.00241

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