Algebraic higher symmetry and local higher fusion category: symmetry as a shadow of topological order

Abstract: I will discuss a most general form of symmetry --algebraic higher symmetry, which include symmetry described by group and higher group. Algebraic higher symmetry, in its most general form, is beyond group and higher group. It is described by local higher fusion category. I also discuss a holographic point of view for symmetry: symmetry is a shadow of topological order in one higher dimension (ie a fusion higher category with trivial center).

Mathematics

Audience: researchers in the topic

( video )

ICCM 2020