A characterization of depth 2 subfactors of II_1 factors
Quantum Algebra
2007-05-23 v2 Operator Algebras
Abstract
We characterize finite index depth 2 inclusions of type II_1 factors in terms of actions of weak Kac algebras and weak C*-Hopf algebras. If N\subset M \subset M_1 \subset M_2 \subset ... is the Jones tower constructed from such an inclusion N\subset M, then B=M^\prime \cap M_2 has a natural structure of a weak C*-Hopf algebra and there is a minimal action of B on M_1 such that M is the fixed point subalgebra of M_1, and M_2 is isomorphic to the crossed product of M_1 and B. This extends the well-known results for irreducible depth 2 inclusions.
Keywords
Cite
@article{arxiv.math/9810028,
title = {A characterization of depth 2 subfactors of II_1 factors},
author = {D. Nikshych and L. Vainerman},
journal= {arXiv preprint arXiv:math/9810028},
year = {2007}
}
Comments
Latex, 26 pages, more precise statements of Theorems 4.17 and 5.7 given, several minor errors corrected