A Galois Correspondence for II1 Factors and Quantum Groupoids

Abstract

We establish a Galois correspondence for finite quantum groupoid actions on II1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such subfactor is completely and canonically determined by a quantum groupoid and its coideal*-subalgebra. This allows us to express the bimodule category of a subfactor in terms of the representation category of a corresponding quantum groupoid and the principal graph as the Bratteli diagram of an inclusion of certain finite-dimensional C*-algebras related to it. © 2000 Academic Press.