Multiple zeta values and zinbiel algebras

Abstract: We will explain the construction, using the notion of Zinbiel algebra, of 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 generating series. 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.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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