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A formula for the logarithm of the KZ associator
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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| dc.contributor.author | Enriquez, B. | |
| dc.contributor.author | Gavarini, F. | |
| dc.date.accessioned | 2019-02-07T09:14:45Z | |
| dc.date.available | 2019-02-07T09:14:45Z | |
| dc.date.issued | 2006 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2000 Mathematics Subject Classification: 17B01; 81R50 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/146087 | |
| dc.description.abstract | 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). | uk_UA |
| dc.description.sponsorship | 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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | A formula for the logarithm of the KZ associator | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
