The general theory of superselection sectors is shown to provide almost all the structure
observed in two-dimensional conformal field theories. Its application to two-dimensional …

We develop a theory of module categories over monoidal categories (this is a
straightforward categorization of modules over rings). As applications we show that any …

We formulate rational conformal field theory in terms of a symmetric special Frobenius
algebra A and its representations. A is an algebra in the modular tensor category of Moore …

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 start the general structure theory of not necessarily semisimple finite tensor categories,
generalizing the results in the semisimple case (ie for fusion categories), obtained recently …

A two-sided coaction of a Hopf algebra on an associative algebra ℳ is an algebra map of the
form, where (λ, ρ) is a commuting pair of left and right-coactions on ℳ, respectively. Denoting …

Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise
quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons …

Noncommutative geometry provides a powerful tool for regularizing quantum field theories
in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling …

By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the
coassociative coproduct to be nonunital, we obtain a quantum group, that we call a weak C …

A comprehensive introduction to two-dimensional conformal field theory is given. The
structure of the meromorphic subtheory is described in detail, and a number of examples are …