Geodesic
Zinbiel algebras and multiple zeta values
Documenta mathematica, Tome 27 (2022), pp. 519-533

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We build, using the notion of Zinbiel algebra, some commutative subalgebras Cu,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 Cu,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.
DOI : 10.4171/dm/876
Classification : 11M32, 17A50, 68R15
Mots-clés : multiple zeta values, Zinbiel algebra, shuffle algebra 
Frédéric Chapoton. Zinbiel algebras and multiple zeta values. Documenta mathematica, Tome 27 (2022), pp. 519-533. doi: 10.4171/dm/876
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     author = {Fr\'ed\'eric Chapoton},
     title = {Zinbiel algebras and multiple zeta values},
     journal = {Documenta mathematica},
     pages = {519--533},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/876},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/876/}
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