A. We classify C∗ near-group categories by using Vaughan Jones theory of subfactors and
the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between …

Quantum field theory has various projective characteristics which are captured by what are
called anomalies. This paper explores this idea in the context of fully-extended three …

A bstract In a physical system undergoing a continuous quantum phase transition,
spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to …

In this paper we construct two new fusion categories and many new subfactors related to the
exceptional Extended Haagerup subfactor. The Extended Haagerup subfactor has two even …

Much of the early work on Fusion Categories was inspired by physicists' desire for rigorous
foundations of topological quantum field theory. One effect of this was that base fields other …

The classification of subfactors of small index revealed several new subfactors. The first
subfactor above index 4, the Haagerup subfactor, is increasingly well understood and …

This paper is the first of a pair that aims to classify a large number of the type $ II $ quantum
subgroups of the categories $\mathcal {C}(\mathfrak {sl} _ {r+ 1}, k) $. In this work we classify …

We further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the
$\mathcal {C} $-based equivalences between two $ G $-graded extensions of $\mathcal {C} …

In this note, we discuss the notion of symmetric self-duality of shaded planar algebras, which
allows us to lift shadings on subfactor planar algebras to obtain Z/2Z-graded unitary fusion …

A tensor category $\mathcal {C} $ over a field $\mathbb {K} $ is said to be invertible if there's
a tensor category $\mathcal {D} $ such that $\mathcal {C}\boxtimes\mathcal {D} $ is Morita …