A Mathematical Curiosity — IV — The Triple Hopf Structure on H₀(Ã₂)
Abstract
This work introduces a quasi-Hopf algebra structure on the 0-Hecke monoid H₀(Ã₂), characterized by three phase-twisted coproducts related by cyclic ℤ₃ symmetry. The idempotence constraint necessarily yields a complex coupling constant λ = (-1 + i√7)/2, and the structure exhibits non-trivial coassociativity governed by a 3-cocycle associator in the sense of Drinfeld.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 19 January 2026