Mixed Pentagon, octagon and Broadhurst duality equation

Details Mixed Pentagon, octagon and Broadhurst duality equation Mixed Pentagon, octagon and Broadhurst duality equation

2011-03-07

arxiv.org/abs/1103.1188v2

Mathematics

Quantum Algebra

20 pages, 1 figure

Scientific paper

This paper is on elimination of defining equations of the cyclotomic analogues, introduced by the first author, of Drinfeld's scheme of associators. We show that the mixed pentagon equation implies the octagon equation for N=2 and the particular distribution relation. We also explain that Broadhurst duality is compatible with the torsor structure. We develop a formalism of infinitesimal module categories and use it for deriving a proof left implicit in the first named author's earlier work.

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