scholarly journals Boundaries of reduced free group C*-algebras

2006 ◽  
Vol 39 (1) ◽  
pp. 35-38 ◽  
Author(s):  
Narutaka Ozawa
Keyword(s):  
Free Group ◽  
C Algebras

Free group C*-algebras associated with ℓp

2014 ◽  
Vol 25 (07) ◽  
pp. 1450065 ◽  
Author(s):  
Rui Okayasu
Keyword(s):  
Free Group ◽  
Positive Definite ◽  
Positive Definite Functions ◽  
Linear Functionals ◽  
C Algebra ◽  
Tracial State ◽  
C Algebras ◽  
Positive Linear Functionals ◽  
The Ideal

For every p ≥ 2, we give a characterization of positive definite functions on a free group with finitely many generators, which can be extended to positive linear functionals on the free group C*-algebra associated with the ideal ℓp. This is a generalization of Haagerup's characterization for the case of the reduced free group C*-algebra. As a consequence, the canonical quotient map between the associated C*-algebras is not injective, and they have a unique tracial state.

scholarly journals C*-algebras of infinite real rank

2002 ◽  
Vol 66 (3) ◽  
pp. 487-496
Author(s):  
A. Chigogidze ◽  
V. Valov
Keyword(s):  
Compact Space ◽  
Free Group ◽  
Real Rank ◽  
Countable Number ◽  
C Algebras ◽  
Number Of Generators

We introduce the notion of weakly (strongly) infinite real rank for unital C*-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C (X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C*-algebra C* (∞) of the free group on countable number of generators has strongly infinite real rank.

scholarly journals P-Tensor Product for Group C*-Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 627
Author(s):  
Yufang Li ◽  
Zhe Dong
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Discrete Group ◽  
Tensor Products ◽  
Haagerup Property ◽  
C Algebras ◽  
P Tensor

In this paper, we introduce new tensor products ⊗ p ( 1 ≤ p ≤ + ∞ ) on C ℓ p * ( Γ ) ⊗ C ℓ p * ( Γ ) and ⊗ c 0 on C c 0 * ( Γ ) ⊗ C c 0 * ( Γ ) for any discrete group Γ . We obtain that for 1 ≤ p < + ∞ C ℓ p * ( Γ ) ⊗ m a x C ℓ p * ( Γ ) = C ℓ p * ( Γ ) ⊗ p C ℓ p * ( Γ ) if and only if Γ is amenable; C c 0 * ( Γ ) ⊗ m a x C c 0 * ( Γ ) = C c 0 * ( Γ ) ⊗ c 0 C c 0 * ( Γ ) if and only if Γ has Haagerup property. In particular, for the free group with two generators F 2 we show that C ℓ p * ( F 2 ) ⊗ p C ℓ p * ( F 2 ) ≇ C ℓ q * ( F 2 ) ⊗ q C ℓ q * ( F 2 ) for 2 ≤ q < p ≤ + ∞ .

$C^*$-algebras of directed graphs and group actions

1999 ◽  
Vol 19 (6) ◽  
pp. 1503-1519 ◽  
Author(s):  
ALEX KUMJIAN ◽  
DAVID PASK
Keyword(s):  
Directed Graph ◽  
Free Group ◽  
Connected Graph ◽  
Dimensional Space ◽  
Directed Graphs ◽  
Free Action ◽  
Crossed Product ◽  
C Algebra ◽  
C Algebras ◽  
Morita Equivalent

Given a free action of a group $G$ on a directed graph $E$ we show that the crossed product of $C^* (E)$, the universal $C^*$-algebra of $E$, by the induced action is strongly Morita equivalent to $C^* (E/G)$. Since every connected graph $E$ may be expressed as the quotient of a tree $T$ by an action of a free group $G$ we may use our results to show that $C^* (E)$ is strongly Morita equivalent to the crossed product $C_0 ( \partial T ) \times G$, where $\partial T$ is a certain zero-dimensional space canonically associated to the tree.

Stable Rank of Some Full Group C*-Algebras of Groups Obtained by the Free Product

1997 ◽  
Vol 08 (03) ◽  
pp. 375-382 ◽  
Author(s):  
Masaru Nagisa
Keyword(s):  
Free Product ◽  
Free Group ◽  
Finite Groups ◽  
Stable Rank ◽  
Real Rank ◽  
Full Group ◽  
The Real ◽  
C Algebras

We compute the real rank and the stable rank of full group C*-algebras. Main result is (i) rr (C*(Fn)) = ∞, (ii) sr (C*(G1 * G2)) = ∞(|G1| ≥ 2, |G2| ≥ 2 and |G1| + |G2| ≥ 5), (iii) sr (C*(G1 * G2)) = 1(|G1| = |G2| = 2), where Fn is the free group with n generators, G1 and G2 are finite groups and |G| means the order of the group G.

scholarly journals PURE STATES ON FREE GROUP C*-ALGEBRAS

2009 ◽  
Vol 52 (1) ◽  
pp. 151-154 ◽  
Author(s):  
CHARLES AKEMANN ◽  
SIMON WASSERMANN ◽  
NIK WEAVER
Keyword(s):  
Free Group ◽  
C Algebra ◽  
C Algebras ◽  
Pure States

AbstractWe prove that all the pure states of the reduced C*-algebra of a free group on an uncountable set of generators are *-automorphism equivalent and extract some consequences of this fact.

scholarly journals Boundary Action On Simple Reduced Group C*-Algebras

2021 ◽  
Vol 03 (01) ◽  
pp. 1-15
Author(s):  
V.A. Onuche ◽  
◽  
T.J Alabiand ◽  
O.F. Ajayi ◽  
◽  
...  
Keyword(s):  
Simple Group ◽  
Free Group ◽  
Discrete Group ◽  
Crossed Products ◽  
Ideal Structure ◽  
Stability Properties ◽  
C Algebras ◽  
Reduced Group ◽  
The Stability

A connection between boundary actions, ideal structure of reduced crossed products and C*-simple group is imminent.We investigate the stability properties for discrete group pioneered by powers and show that the non-abelian free group on two generators is C*-simple.Kalantar and Kennedy [32, Theorem 6.2] is now extended. Some examples are given using characterization of C*-simplicity obtained by Kalantar, Kennedy, Breuillard, and Ozawa [10, Theorem 3.1]

scholarly journals NON-COCOMMUTATIVE C*-BIALGEBRA DEFINED AS THE DIRECT SUM OF FREE GROUP C*-ALGEBRAS

2015 ◽  
Vol 58 (1) ◽  
pp. 119-136
Author(s):  
KATSUNORI KAWAMURA
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Free Groups ◽  
Full Group ◽  
C Algebras ◽  
Direct Sum ◽  
Product Formulas

AbstractLeti ${\Bbb F}$n be the free group of rank n and let $\bigoplus C^{*}({\Bbb F}_{n})$ denote the direct sum of full group C*-algebras $C^{*}({\Bbb F}_{n})$ of ${\Bbb F}_{n} (1\leq n<\infty$). We introduce a new comultiplication Δϕ on $\bigoplus C^{*}({\Bbb F}_{n})$ such that $(\bigoplus C^{*}({\Bbb F}_{n}),\,\Delta_{\varphi})$ is a non-cocommutative C*-bialgebra. With respect to Δϕ, the tensor product π⊗ϕπ′ of any two representations π and π′ of free groups is defined. The operation ×ϕ is associative and non-commutative. We compute its tensor product formulas of several representations.

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