Infinite multiplicity of abelian subalgebras in free group subfactors
Abstract
We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a ${II}_1$factor $\mc{M}$ with a subfactor $\mc{N}$ containing an abelian subalgebra $\mc{A}$ of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402107
 Bibcode:
 2004math......2107S
 Keywords:

 Operator Algebras;
 46Lxx (Primary) 47Lxx (Secondary)