Citation: Bischoff, Marcel. "The rank of G-crossed braided extensions of modular tensor categories." Topological phases of matter and quantum computation. Vol. 747. Amer. Math. Soc.[Providence], RI, 2020. 115-119.
Web: https://arxiv.org/abs/1807.06131
Tags: Mathematical, Modular-tensor-categories, SPT/SETs
One of the most useful formulas in the theory of G-crossed modular tensor categories is an explicit formula for the rank of each component in the extension. The standard proof comes from the non-degeneracy of the matrix - the fact that the S-matrix is an isomorphism means that it must be an isomorphism on each component, and counting the dimensions of each component gives the answer. This paper gives a nice alternative one-page proof in terms of Lagrangian algebras. When writing a book-treatment or review of G-crossed MTCs, this is definitely a paper to keep in mind for perhaps pedagogical reasons.