Pentagon and hexagon equations

By H. Furusho. 2007

83 citations recorded by the source corpus.

The author will prove that Drinfel’d’s pentagon equation implies his two hexagon equations in the Lie algebra, pro-unipotent, pro-l and pro-nilpotent contexts.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/87ec71e5dea94d16be3208ff09a8dc11f1a09aa8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. A. Alekseev
2. Thomas Willwacher
3. C. Torossian
4. R. Mehta

In Geometry and Topology

1. A. Alekseev
2. Thomas Willwacher
3. C. Torossian
4. R. Mehta

In Statistical and Nonlinear Physics

1. A. Alekseev
2. Thomas Willwacher
3. C. Torossian

Citations in the corpus

• The Kashiwara-Vergne conjecture and Drinfeld’s associators (2008, background): “Remark 9.4. For Drinfeld’s associators, Furusho [ 12 ] showed that the hexagon equations (31), (32) and the inversion property (30) follow from the pentagon equation and the normalization condition �(�2) = 1/8.”
• M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra (2010, background): “reducing to this subcomplex at the first step, the inclusion is a quasi-isomorphism. The author learned this trick from P. ˇSevera. Appendix C. (Re-)Derivation of Furusho’sresult In a remarkable paper [9], H. Furusho showed that the Hexagon equation (4) is a consequence of the Pentagon equation (3), ”