Motivic coaction and single-valued map of polylogarithms from zeta generators
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912029666705408 |
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| author | Frost, Hadleigh Hidding, Martijn Kamlesh, Deepak Rodriguez, Carlos Schlotterer, Oliver Verbeek, Bram |
| author_facet | Frost, Hadleigh Hidding, Martijn Kamlesh, Deepak Rodriguez, Carlos Schlotterer, Oliver Verbeek, Bram |
| contents | We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00697 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Motivic coaction and single-valued map of polylogarithms from zeta generators Frost, Hadleigh Hidding, Martijn Kamlesh, Deepak Rodriguez, Carlos Schlotterer, Oliver Verbeek, Bram High Energy Physics - Theory Algebraic Geometry Number Theory We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by conjugating generating series of polylogarithms with Lie-algebra generators associated with odd zeta values. Our reformulation of earlier constructions of coactions and single-valued polylogarithms preserves choices of fibration bases, exposes the correlation between multiple zeta values of different depths and paves the way for generalizations beyond genus zero. |
| title | Motivic coaction and single-valued map of polylogarithms from zeta generators |
| topic | High Energy Physics - Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2312.00697 |