scholarly journals Purely Infinite, Simple $C^*$-Algebras Arising from Free Product Constructions, II

2002 ◽  
Vol 90 (1) ◽  
pp. 73 ◽  
Author(s):  
Kenneth J. Dykema
Keyword(s):  
Free Product ◽  
Free Products ◽  
C Algebras

Certain reduced free products of $C^*$-algebras with respect to faithful states are simple and purely infinite.

scholarly journals ON THE STRUCTURE OF SOME REDUCED AMALGAMATED FREE PRODUCT C*-ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 281-306 ◽  
Author(s):  
NIKOLAY A. IVANOV
Keyword(s):  
Free Product ◽  
Sufficient Conditions ◽  
Positive Cone ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Free Products ◽  
C Algebras ◽  
Amalgamated Free Product ◽  
Necessary And Sufficient

We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the latter result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag–Solitar groups BS(m, n).

scholarly journals Purely Infinite, Simple C*-Algebras Arising From Free Product Constructions

1998 ◽  
Vol 50 (2) ◽  
pp. 323-341 ◽  
Author(s):  
Kenneth J. Dykema ◽  
Mikael Rørdam
Keyword(s):  
Free Product ◽  
List Type ◽  
Crossed Products ◽  
Type Number ◽  
Free Products ◽  
C Algebras

AbstractExamples of simple, separable, unital, purely infinite C*-algebras are constructed, including:(1)some that are not approximately divisible;(2)those that arise as crossed products of any of a certain class of C*-algebras by any of a certain class of non–unital endomorphisms;(3)those that arise as reduced free products of pairs of C*-algebras with respect to any from a certain class of states.

scholarly journals Topological Free Entropy Dimensions in Nuclear C*-algebras and in Full Free Products of Unital C*-algebras

2011 ◽  
Vol 63 (3) ◽  
pp. 551-590 ◽  
Author(s):  
Don Hadwin ◽  
Qihui Li ◽  
Junhao Shen
Keyword(s):  
Free Product ◽  
Finite Family ◽  
Free Products ◽  
C Algebra ◽  
Free Entropy ◽  
C Algebras ◽  
Entropy Dimension ◽  
Free Entropy Dimension

Abstract In the paper, we introduce a new concept, topological orbit dimension of an n-tuple of elements in a unital C*-algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear C*-algebra is less than or equal to 1. We also show that the Voiculescu's topological free entropy dimension is additive in the full free product of some unital C*-algebras. We show that the unital full free product of Blackadar and Kirchberg's unital MF algebras is also an MF algebra. As an application, we obtain that Ext(C*r (F2) *C C* r (F2)) is not a group.

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Free product decompositions in images of certain free products of groups

2007 ◽  
Vol 310 (1) ◽  
pp. 57-69
Author(s):  
N.S. Romanovskii ◽  
John S. Wilson
Keyword(s):  
Free Product ◽  
Free Products ◽  
Products Of Groups

On Unital Full Amalgamated Free Products of Quasidiagonal C*-Algebras

2016 ◽  
Vol 50 (1) ◽  
pp. 39-47
Author(s):  
Qihui Li ◽  
Don Hadwin ◽  
Jiankui Li ◽  
Xiujuan Ma ◽  
Junhao Shen
Keyword(s):  
Free Products ◽  
C Algebras ◽  
Amalgamated Free Products

Groups in which every Finitely Generated Subgroup is almost a Free Factor

1979 ◽  
Vol 31 (6) ◽  
pp. 1329-1338 ◽  
Author(s):  
A. M. Brunner ◽  
R. G. Burns
Keyword(s):  
Free Product ◽  
Free Group ◽  
Finite Index ◽  
Finitely Generated ◽  
Free Products

In [5] M. Hall Jr. proved, without stating it explicitly, that every finitely generated subgroup of a free group is a free factor of a subgroup of finite index. This result was made explicit, and used to give simpler proofs of known results, in [1] and [7]. The standard generalization to free products was given in [2]: If, following [13], we call a group in which every finitely generated subgroup is a free factor of a subgroup of finite index an M. Hall group, then a free product of M. Hall groups is again an M. Hall group. The recent appearance of [13], in which this result is reproved, and the rather restrictive nature of the property of being an M. Hall group, led us to attempt to determine the structure of such groups. In this paper we go a considerable way towards achieving this for those M. Hall groups which are both finitely generated and accessible.

scholarly journals Orders on Trees and Free Products of Left-ordered Groups

2020 ◽  
Vol 63 (2) ◽  
pp. 335-347
Author(s):  
Warren Dicks ◽  
Zoran Šunić
Keyword(s):  
Free Product ◽  
Short Proof ◽  
Free Products ◽  
Ordered Groups ◽  
Vertex Set ◽  
Total Orders

AbstractWe construct total orders on the vertex set of an oriented tree. The orders are based only on up-down counts at the interior vertices and the edges along the unique geodesic from a given vertex to another.As an application, we provide a short proof (modulo Bass–Serre theory) of Vinogradov’s result that the free product of left-orderable groups is left-orderable.

Residual finiteness of free products of combinatorial strict inverse semigroups

1994 ◽  
Vol 124 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Karl Auinger
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Inverse Semigroups ◽  
Residual Finiteness ◽  
Free Products ◽  
Residually Finite

It is shown that the free product of two residually finite combinatorial strict inverse semigroups in general is not residually finite. In contrast, the free product of a residually finite combinatorial strict inverse semigroup and a semilattice is residually finite.

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