A subtheory of a quantum field theory specifies von Neumann subalgebras (the
'observables' in the space-time region) of the von Neumann algebras (the'field'localized in) …

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 …

Is there a vector space whose dimension is the golden ratio? Of course not--the golden ratio
is not an integer! But this can happen for generalizations of vector spaces--objects of a …

We give an introduction to the theory of weak Hopf algebras proposed as a coassociative
alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as close …

We consider certain categorical structures that are implicit in subfactor theory. Making the
connection between subfactor theory (at finite index) and category theory explicit sheds light …

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 …

This book provides an introduction to the theory of quantum groups with emphasis on their
duality and on the setting of operator algebras. Part I of the text presents the basic theory of …

In which a theory of dimension related to the Jones index and based on the notion of
conjugation is developed. An elementary proof of the additivity and multiplicativity of the …

We describe the structure of the inclusions of factors?(E)⊂?(E′)′ associated with multi-
intervals E⊂ ℝ for a local irreducible net? of von Neumann algebras on the real line …

A subfactor is an inclusion $ N\subset M $ of von Neumann algebras with trivial centers. The
simplest example comes from the fixed points of a group action $ M^ G\subset M $, and …