As an application of the general theory established in the first part, we determine the
structure of Longo–Rehren inclusions for several systems of sectors arising from …

Let K be a commutative ring with unit. For a K-linear endomorphism f: X! X of a free K-
module of ˇnite rank X, we have the usual trace Tr (f) 2 K deˇned as the trace of the matrix of f …

For every tensor category C there is a braided tensor category Z (C), the 'center'of C. It is well
known to be related to Drinfel'd's notion of the quantum double of a finite dimensional Hopf …

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Braided tensor categories [18] play a central roÃle in the representation theory of quantum
groups [9, 19], of Kac±Moody algebras [21], and of quantum field theories [14, 24]. They also …

Moonshine forms a way of explaining the mysterious connection between the monster finite
group and modular functions from classical number theory. The theory has evolved to …

In topological quantum computing, information is encoded in “knotted” quantum states of
topological phases of matter, thus being locked into topology to prevent decay. Topological …

We calculate the analytic form of the vacuum modular Hamiltonian for a two interval region
and the algebra of a current j (x)=∂ ϕ (x) corresponding to a chiral free scalar ϕ in d= 2. We …

We completely classify diffeomorphism covariant local nets of von Neumann algebras on the
circle with central charge c less than 1. The irreducible ones are in bijective correspondence …

A bstract Some quantum field theories show, in a fundamental or an effective manner, an
alternative between a loss of duality for algebras of operators corresponding to …