home | literature reviews

## "On generalized symmetries and structure of modular categories", Shawn Cui, Modjtaba Zini, Zhenghan Wang, 2019

*Reviewed January 15, 2024*

*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.