Tensor Categories and Endomorphisms of von Neumann Algebras: with Applications to Quantum Field Theo

Introduction.- Homomorphisms of von Neumann algebras.- Endomorphisms of infinite factors.- Homomorphisms and subfactors.- Non-factorial extensions.- Frobenius algebras, Q-systems and modules.- C* Frobenius algebras.- Q-systems and extensions.- The canonical Q-system.- Modules of Q-systems.- Induced Q-systems and Morita equivalence.- Bimodules.- Tensor product of bimodules.- Q-system calculus.- Reduced Q-systems.- Central decomposition of Q-systems.- Irreducible decomposition of Q-systems.- Intermediate Q-systems.- Q-systems in braided tensor categories.- a-induction.- Mirror Q-systems.- Centre of Q-systems.- Braided product of Q-systems.- The full centre.- Modular tensor categories.- The braided product of two full centres.- Applications in QFT.- Basics of algebraic quantum field theory.- Hard boundaries.- Transparent boundaries.- Further directions.- Conclusions.