A formula for the logarithm of the KZ associator
We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator Φ to derive a formula for log(Φ) in terms of MZV's (multiple zeta values)....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146087 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A formula for the logarithm of the KZ associator / B. Enriquez, F. Gavarini // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 4 назв. — англ. |
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Enriquez, B. Gavarini, F. 2019-02-07T09:14:45Z 2019-02-07T09:14:45Z 2006 A formula for the logarithm of the KZ associator / B. Enriquez, F. Gavarini // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 4 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B01; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/146087 We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator Φ to derive a formula for log(Φ) in terms of MZV's (multiple zeta values). This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We first established the formula for log(Φ) in Corollary 1 by analytic computations (using a direct proof of Lemma 2). It was the referee who remarked its formal similarity with the formula of Le and Murakami (Theorem 1); this remark can be expressed as the equality log(Φ) = cbh d2(Φ). This led us to try and understand whether this formula followed from the group-likeness of Φ, which is indeed the case (Proposition 1). C. Reutenauer then pointed out that a part of our argument is a result in his book. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A formula for the logarithm of the KZ associator Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A formula for the logarithm of the KZ associator |
| spellingShingle |
A formula for the logarithm of the KZ associator Enriquez, B. Gavarini, F. |
| title_short |
A formula for the logarithm of the KZ associator |
| title_full |
A formula for the logarithm of the KZ associator |
| title_fullStr |
A formula for the logarithm of the KZ associator |
| title_full_unstemmed |
A formula for the logarithm of the KZ associator |
| title_sort |
formula for the logarithm of the kz associator |
| author |
Enriquez, B. Gavarini, F. |
| author_facet |
Enriquez, B. Gavarini, F. |
| publishDate |
2006 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for the Knizhnik-Zamolodchikov (KZ) associator Φ to derive a formula for log(Φ) in terms of MZV's (multiple zeta values).
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146087 |
| citation_txt |
A formula for the logarithm of the KZ associator / B. Enriquez, F. Gavarini // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 4 назв. — англ. |
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| first_indexed |
2025-12-01T15:27:13Z |
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2025-12-01T15:27:13Z |
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