Weak Hopf C*-algebras and depth two subfactors

摘要

We prove that for a finite index and depth two inclusion N subset of M of III factors, the relative commutants N' boolean AND M-1 and M' boolean AND M-2 admit mutually dual weak Hopf C*-algebra structures. The proof is based on 'planar algebra techniques'. In the hyperfinite case, one can show that N' boolean AND M-1 acts on M with invariants N using this approach. (C) 2004 Elsevier Inc. All rights reserved.