Two subfactors and the algebraic decomposition of bimodules over II\(_1\) factors. (English) Zbl 1182.46049

Jones, Vaughan F. R.

Acta Math. Vietnam. 33, No. 3, 209-218 (2008).

Summary: It is shown that the Hilbert space decomposition of a bifinite correspondence between II\(_1\) factors (in the sense of Connes) is the same as the purely algebraic decomposition of its bounded vectors. This makes natural the systematic study of pairs of finite index subfactors, for which a combinatorial and a spectral invariant are defined by analogy with the invariants of a pair of closed subspaces of a Hilbert space. Some simple examples are calculated.

MSC:

46L37

Subfactors and their classification

Keywords:

subfactor; Dixmier averaging; planar algebra; correspondence; index