Lattice of intermediate subalgebras of a pair of simple C*-algebras

Abstract: The study of the lattice of intermediate objects of a pair $B \subset A$ in any category is quite a natural and fundamental question and has a significant say in obtaining a better understanding of the structures of the objects A and B. A good deal of work in this direction has been done in the category of finite groups, both of qualitative and quantitave flavour. Its natural analogue in the theory of operator algebras has had some success, though mainly quantitative in nature and based on some existing tools. Continuing the trend, in a recent work with Keshab Chandra Bakshi, we developed certain tools in the category of simple C*-algebras (motivated by and analogous to the ones existing in the category of simple von Neumann algebras) to answer a quantitative question of Roberto Longo regarding the lattice of intermediate von Neumann subalgebras of an inclusion of type III factors. We shall present some essence of this development with an attempt to make the talk accessible to a larger audience.

functional analysisK-theory and homologyoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras