Tensor Categories and Endomorphisms of von Neumann Algebras

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.

"The volume gives a coherent overview of some recent mathematical developments in the study of endomorphisms of von Neumann algebras and their applications in algebraic quantum field theory. ... every chapter has its own list of references, which points the reader to more detailed literature. ... Anyone who wishes to understand the recent advances in our understanding of endomorphisms of von Neumann algebras ... should find this book a valuable resource." (Ko Sanders, Mathematical Reviews, January, 2016)