Citation: Cui, Shawn Xingshan, Modjtaba Shokrian Zini, and Zhenghan Wang. "On generalized symmetries and structure of modular categories." Science China Mathematics 62 (2019): 417-446.
Web: https://arxiv.org/abs/1809.00245
Tags: SPT/SETs, Modular-tensor-categories
This paper introduces a generalized form of symmetry on modular tensor categories, based on the actions of "linear Hopf monads". Linear Hopf monads are far-reaching generalizations of Hopf-algebras, and there is a natural way to define their action on an MTC.
It is clear to many people that there are symmetries of modular tensor categories which are not captured by finite groups alone. An example is given by the authors in the introduction: " One of the motivations for this work is the possibility of generalizing the doubled Haagerup category by gauging some Hopf monad symmetries on abelian modular categories".
Other authors are generalizing in this direction as well, namely, there is a hypergroup based symmetry introduced here:
> Bischoff, Marcel. "Generalized orbifold construction for conformal nets." Reviews in Mathematical Physics 29.01 (2017): 1750002.