Zinbiel algebras and multiple zeta values

2021/09/01 by Frédéric Chapoton, Chapoton, Frédéric · 3 citations
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA

paper · pdf · doi:10.48550/arxiv.2109.00241

11 pages, 1 figure

arxiv created 2021/09/01 · arxiv updated 2021/09/02

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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