Chennai Mathematical Institute


Date: Tuesday, November 24, 2020.
Time: 3:30 PM.
Zoom Meeting Link:
Meeting ID: 859 2331 2360
Passcode: 392843
Lattice of intermediate subalgebras

Keshab Chandra Bakshi
Chennai Mathematical Institute.


It is known that every irreducible pair of simple $C^*$-algebras with a conditional expectation of index-finite type has only finitely many intermediate $C^*$-subalgebras. We provide an explicit bound for the cardinality of this set. To achieve this we have introduced a Fourier theory on the relative commutants of such inclusions and discovered a notion of angle between any two intermediate subalgebras. We have found a uniform 60 to 90 degree bound for the angle between minimal intermediate subalgebras and exploited this rigidity pheonomenon to deduce that the number of minimal intermediate subalgebras is in fact bounded by the kissing number. As a pleasant consequence, we answer a question due to Roberto Longo (published in 2003)regarding intermediate subfactors of an inclusion of type III factors with finite index. This is a part of a recent joint work with Ved Gupta.