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A formula for the logarithm of the KZ associator
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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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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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2, випуск за цей рік
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A formula for the logarithm of the KZ associator
Інший ID:
2000 Mathematics Subject Classification: 17B01; 81R50
Посилання:
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.
Підтримка:
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.
Дата:
2006
Переглядів:
671
Завантажень:
289
Анотація:
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).
