Amalgamated Free Products of Multi-Matrix Algebras and a Construction of Subfactors of a Free Group Factor

1995 ◽  
Vol 117 (6) ◽  
pp. 1555 ◽  
Author(s):  
Kenneth J. Dykema
Keyword(s):  
Free Group ◽  
Group Factor ◽  
Free Products ◽  
Matrix Algebras ◽  
Amalgamated Free Products ◽  
Free Group Factor

scholarly journals Structural results for free Araki–Woods factors and their continuous cores

2010 ◽  
Vol 9 (4) ◽  
pp. 741-767 ◽  
Author(s):  
Cyril Houdayer
Keyword(s):  
Hilbert Space ◽  
Fundamental Group ◽  
Free Group ◽  
Real Hilbert Space ◽  
Group Factor ◽  
Orthogonal Representation ◽  
Type Iii ◽  
The Core ◽  
Free Group Factor

AbstractWe show that for any type III1free Araki–Woods factor$\mathcal{M}$=(HR, Ut)″ associated with an orthogonal representation(Ut)ofRon a separable real Hilbert spaceHR, the continuous coreM=$\mathcal{M}$⋊σRis a semisolid II∞factor, i.e. for any non-zero finite projectionq∈M, the II1factorqM qis semisolid. If the representation(Ut)is moreover assumed to be mixing, then we prove that the coreMis solid. As an application, we construct an example of a non-amenable solid II1factorNwith full fundamental group, i.e.$\mathcal{F}$(N) =R*+, which is not isomorphic to any interpolated free group factorL(Ft), for 1 <t≤ = +∞.

scholarly journals The radial masa in a free group factor is maximal injective

2010 ◽  
Vol 82 (3) ◽  
pp. 787-809 ◽  
Author(s):  
Jan Cameron ◽  
Junsheng Fang ◽  
Mohan Ravichandran ◽  
Stuart White
Keyword(s):  
Free Group ◽  
Group Factor ◽  
Free Group Factor

scholarly journals ON A SUBFACTOR CONSTRUCTION OF A FACTOR NON-ANTIISOMORPHIC TO ITSELF

2004 ◽  
Vol 15 (08) ◽  
pp. 833-854 ◽  
Author(s):  
MARIA GRAZIA VIOLA
Keyword(s):  
Free Group ◽  
Crossed Product ◽  
Group Factor ◽  
Enveloping Algebra ◽  
Inner Automorphism ◽  
Free Group Factor

We define a ℤ3-kernel α on [Formula: see text] and a ℤ3-kernel β on the hyperfinite II 1 factor R, which have conjugate obstruction to lifting. Hence, α⊗β can be perturbed by an inner automorphism to produce an action γ on [Formula: see text]. The aim of this paper is to show that the factor [Formula: see text], which is similar to Connes's example of a II 1 factor non-antiisomorphic to itself, is the enveloping algebra of an inclusion of II 1 factors A⊂B. Here A is an interpolated free group factor and B is isomorphic to the crossed product A⋊θℤ9, where θ is a ℤ3-kernel of A with non-trivial obstruction to lifting. By using an argument due to Connes, which involves the invariant χ(ℳ), we show that ℳ is not anti-isomorphic to itself. Furthermore, we prove that for one of the generator of χ(ℳ), which we will denote by σ, the Jones invariant ϰ(σ) is equal to [Formula: see text].

scholarly journals The Laplacian MASA in a free group factor

2002 ◽  
Vol 355 (2) ◽  
pp. 465-475 ◽  
Author(s):  
Allan M. Sinclair ◽  
Roger R. Smith
Keyword(s):  
Free Group ◽  
Group Factor ◽  
Free Group Factor

A NOTE ON MAXIMAL SUBFACTORS

2010 ◽  
Vol 03 (04) ◽  
pp. 707-713
Author(s):  
Liguang Wang ◽  
Xiujuan Ma
Keyword(s):  
Free Group ◽  
Type I ◽  
Group Factor ◽  
Basic Construction ◽  
Index 2 ◽  
Free Group Factor

In this note, we consider the maximal subfactors of factors. We show that there is no maximal subfactor of type In factors when n is finite. We also consider the relation between maximal subfactor and Jones' basic construction. In the end, we give an example of an index 2 maximal subfactor in free group factor with 2 generators.

scholarly journals ON THE GROWTH OF GROUPS AND AUTOMORPHISMS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 869-874 ◽  
Author(s):  
MARTIN R. BRIDSON
Keyword(s):  
Finitely Generated ◽  
Free Products ◽  
Dehn Functions ◽  
Amalgamated Free Products ◽  
Growth Functions ◽  
Growth Of Groups

We consider the growth functions βΓ(n) of amalgamated free products Γ = A *C B, where A ≅ B are finitely generated, C is free abelian and |A/C| = |A/B| = 2. For every d ∈ ℕ there exist examples with βΓ(n) ≃ nd+1βA(n). There also exist examples with βΓ(n) ≃ en. Similar behavior is exhibited among Dehn functions.

scholarly journals Separating conjugates in amalgamated free products and HNN extensions

1980 ◽  
Vol 29 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Joan L. Dyer
Keyword(s):  
Nilpotent Groups ◽  
Conjugacy Classes ◽  
Free Products ◽  
Amalgamated Free Products ◽  
Hnn Extensions ◽  
Nontrivial Center ◽  
One Relator Groups ◽  
Amalgamated Subgroup ◽  
Conjugacy Separable ◽  
Base Group

AbstractA group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.

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