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What would be a good (as "easy" as possible) example of a Triangular (Non trivial) quasi-Hopf algebra? By trivial I mean the quasi strcture not to be trivial, but if the triangular structure is trivial it's ok (it's actally better for me)

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Something like Drinfeld's twist of a group algebra will do the job.

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You can see the following papers:

S. Majid, "Quantum Double for Quasi-Hopf Algebras",Letters in math. phys., 45, Number 1 , pages 1-9 (1998).

C. A. S. Young, R. Zegers. Triangular quasi-Hopf algebra structures on certain non-semisimple quantum groups, Commun. Math. Phys. 298, 585-611 (2010).

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