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The pentagon equation and the confluence relations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 144, Number 4, August 2022
- pp. 873-894
- 10.1353/ajm.2022.0018
- Article
- Additional Information
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Abstract
Abstract:
We show an equivalence of Drinfeld's pentagon equation and Hirose-Sato's confluence relations. As a corollary, we obtain a `pentagon-free' presentation of the Grothendieck-Teichm\"{u}ller group $GRT_1$ and associators.
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