On a question of Vaughan Jones

Abstract: Given a subgroup H of a finite group G, as an application of famous Hall's Marriage Theorem, we can obtain a set of coset representatives which acts simultaneously as representatives of both left and right cosets of H in G. Given a subfactor $N\subset M$ with finite Jones index, M can be regarded as a left as well as a right N-module. Pimsner and Popa proved that M is finitely generated as a left (equivalently, right) N-module. About a decade back, Vaughan Jones asked whether one can find a common set which acts simultaneously as a left and a right generating set. As a naive attempt in this direction, we answer this question in the affirmative for a large class of integer index subfactors. We also discuss some applications of our results.

functional analysisK-theory and homologyoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras