Construction of type II1 factors with prescribed countable fundamental group
Abstract
In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type II1 with prescribed countable fundamental group. First we investigate state-preserving group actions on the almost periodic free Araki-Woods factors satisfying both a condition of mixing and a condition of free malleability in the sense of Popa. Typical examples are given by the free Bogoliubov shifts. Take an ICC w-rigid group G such that ℱ(L(G)) = {1} (e.g., G = ℤ2 ⋊ SL(2, ℤ)). For any countable subgroup S ⊂ 
, we construct an action of G on L(𝔽∞) such that the associated crossed product L(𝔽∞) ⋊ G is a type II1 factor and its fundamental group is S. The second construction is based on a free product. Take (B(H),ψ) any factor of type I endowed with a faithful normal state and denote by S ⊂ the subgroup generated by the point spectrum of ψ. We show that the centralizer (L(G) ∗ B(H))τ*ψ is a type II1 factor and its fundamental group is S. Our proofs rely on Popa's deformation/rigidity strategy using his intertwining-by-bimodules technique.
© Walter de Gruyter Berlin · New York 2009
Articles in the same Issue
- On the stable trace formula for Sp4
- Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
- Deformation theory of representations of prop(erad)s I
- Normes invariantes et existence de filtrations admissibles
- Relaxation of the flow of triods by curve shortening flow via the vector-valued parabolic Allen-Cahn equation
- Construction of type II1 factors with prescribed countable fundamental group
- Prym-Tyurin varieties via Hecke algebras
Articles in the same Issue
- On the stable trace formula for Sp4
- Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables
- Deformation theory of representations of prop(erad)s I
- Normes invariantes et existence de filtrations admissibles
- Relaxation of the flow of triods by curve shortening flow via the vector-valued parabolic Allen-Cahn equation
- Construction of type II1 factors with prescribed countable fundamental group
- Prym-Tyurin varieties via Hecke algebras
