Idempotents in the Reduced C ∗ -Algebra of a Free Group

1988 ◽  
Vol 103 (3) ◽  
pp. 779
Author(s):  
Joel M. Cohen ◽  
Alessandro Figa-Talamanca
Keyword(s):  
Free Group ◽  
C Algebra

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.

$C^*$-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.

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 On some “stability” properties of the full C*-algebra associated to the free group F∞

1998 ◽  
Vol 41 (1) ◽  
pp. 93-116 ◽  
Author(s):  
Asma Harcharras
Keyword(s):  
Tensor Product ◽  
Free Group ◽  
Extension Property ◽  
The Other ◽  
Operator Space ◽  
Complex Interpolation ◽  
Stability Properties ◽  
C Algebra ◽  
Other Hand

Let C*(F∞) be the full C*-algebra associated to the free group of countably many generators and SnC*(F∞) be the class of all n-dimensional operator subspaces of C*(F∞). In this paper, we study some stability properties of SnC*(F∞). More precisely, we will prove that for any E0, E1 in SnC*(F∞), the Haagerup tensor product E0⊗hE1 and the operator space obtained by complex interpolation Eθ are (1 + ∈)-contained in C*(F∞) for arbitrary ∈>0. On the other hand, we will show an extension property for WEPC*-algebras.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals The Poincaré half-space of a C$^*$-algebra

2019 ◽  
Vol 35 (7) ◽  
pp. 2187-2219
Author(s):  
Esteban Andruchow ◽  
Gustavo Corach ◽  
Lázaro Recht
Keyword(s):  
Half Space ◽  
C Algebra

scholarly journals Embedding the Picard group inside the class group: the case of $$\mathbb {Q}$$-factorial complete toric varieties

2021 ◽  
Author(s):  
Michele Rossi ◽  
Lea Terracini
Keyword(s):  
Free Group ◽  
Toric Variety ◽  
Class Group ◽  
Abelian Groups ◽  
Toric Varieties ◽  
Picard Group ◽  
Closed Field ◽  
Finitely Generated ◽  
Free Part ◽  
Canonical Injection

AbstractLet X be a $$\mathbb {Q}$$ Q -factorial complete toric variety over an algebraic closed field of characteristic 0. There is a canonical injection of the Picard group $$\mathrm{Pic}(X)$$ Pic ( X ) in the group $$\mathrm{Cl}(X)$$ Cl ( X ) of classes of Weil divisors. These two groups are finitely generated abelian groups; while the first one is a free group, the second one may have torsion. We investigate algebraic and geometrical conditions under which the image of $$\mathrm{Pic}(X)$$ Pic ( X ) in $$\mathrm{Cl}(X)$$ Cl ( X ) is contained in a free part of the latter group.

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