English

Inclusions of von Neumann Algebras and Quantum groupoids III

Operator Algebras 2007-05-23 v1 Quantum Algebra

Abstract

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two "quantum groupo\"{\i}ds" dual to each other, from a depth 2 inclusion of von Neumann algebras M0M1M_0\subset M_1, in such a way that the canonical Jones'tower associated to the inclusion can be described as a tower of successive crossed-products by these two structures. We are now investigating in greater details these structures in the presence of an appropriate modular theory on the basis M0M1M'_0\cap M_1, and we show how these examples fit with Lesieur's "measured quantum groupo\"{\i}ds".

Keywords

Cite

@article{arxiv.math/0405480,
  title  = {Inclusions of von Neumann Algebras and Quantum groupoids III},
  author = {Michel Enock},
  journal= {arXiv preprint arXiv:math/0405480},
  year   = {2007}
}