Paulo R. Pinto

Subfactor Realisation of Modular Invariants

Abstract: We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is a useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D5(1). In particular for the double of S3, 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors.

Orbit Representations and Circle Maps

We yield C*-algebras representations on the orbit spaces from the family of interval maps f(x) = βx+α (mod 1) lifted to circle maps, in which case β ∈ N.

Subfactor realization of modular invariants: II

We use the subfactor approach to study in detail the realization of the modular invariants of the double of the symmetric group S3 at all twists w ∈ Z3(S3, 𝕋) and of the Haagerup subfactor, correcting an error in our previous work.

Twisted quantum modular data and braided subfactors

The modular data from twisted quantum double of finite groups G are studied, with cyclic groups. It is proved that the [k] and [ − k] modular data are the same up to relabelling of the primary fields and complex conjugation of the underlying representation of the modular group . Then we produce some lower bounds for the number of modular invariants of these models, and complete the study for the cases and at all twists, proving in particular that all their modular invariants are produced by braided subfactors.

Amenable Crossed Product Banach Algebras Associated with a Class of \(\varvec{{\mathrm C}^*}\)-Dynamical Systems

We prove that the crossed product Banach algebra

Modular invariants and their fusion rules

\ell ^1(G,A;\alpha )

Simple current modular invariants from braided subfactors

ℓ1(G,A;α) that is associated with a