scholarly journals KK-Equivalence for Amalgamated Free Product C*-Algebras

2016 ◽  
Vol 2016 (24) ◽  
pp. 7619-7636 ◽  
Author(s):  
Kei Hasegawa
Keyword(s):  
Free Product ◽  
C Algebras ◽  
Amalgamated Free Product

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 On embeddings of full amalgamated free product C$^*$–algebras

2004 ◽  
Vol 132 (7) ◽  
pp. 2019-2030 ◽  
Author(s):  
Scott Armstrong ◽  
Ken Dykema ◽  
Ruy Exel ◽  
Hanfeng Li
Keyword(s):  
Free Product ◽  
C Algebras ◽  
Amalgamated Free Product

scholarly journals Bass–Serre Trees of Amalgamated Free Product C*-algebras

2018 ◽  
Vol 2019 (21) ◽  
pp. 6529-6553 ◽  
Author(s):  
Kei Hasegawa
Keyword(s):  
Free Product ◽  
Crossed Product ◽  
Approximation Properties ◽  
C Algebra ◽  
Product Group ◽  
C Algebras ◽  
Amalgamated Free Product

Abstract For any reduced amalgamated free product C*-algebra (A, E) = (A1, E1) *D(A2, E2), we introduce and study a canonical ambient C*-algebra ΔT (A, E) of A which generalizes the crossed product arising from the canonical action of an amalgamated free product group on the compactification of the associated Bass–Serre tree. Using an explicit identification of ΔT (A, E) with a Cuntz–Pimsner algebra we prove two kinds of “amenability” results for ΔT (A, E); nuclearity and universality. As applications of our framework, we provide new conceptual, and simpler proofs of several known theorems on approximation properties, embeddability, and KK-theory for reduced amalgamated free product C*-algebras.

scholarly journals Amalgamated free product rigidity for group von Neumann algebras

2018 ◽  
Vol 329 ◽  
pp. 819-850 ◽  
Author(s):  
Ionuţ Chifan ◽  
Adrian Ioana
Keyword(s):  
Free Product ◽  
Von Neumann Algebras ◽  
Von Neumann ◽  
Amalgamated Free Product

Amalgamated free product in terms of automata constructions

2021 ◽  
pp. 1-11
Author(s):  
A. S. Oliynyk ◽  
V. A. Prokhorchuk
Keyword(s):  
Free Product ◽  
Amalgamated Free Product

scholarly journals Tensor Product Decompositions of II1 Factors Arising from Extensions of Amalgamated Free Product Groups

2018 ◽  
Vol 364 (3) ◽  
pp. 1163-1194 ◽  
Author(s):  
Ionut Chifan ◽  
Rolando de Santiago ◽  
Wanchalerm Sucpikarnon
Keyword(s):  
Tensor Product ◽  
Free Product ◽  
Amalgamated Free Product

scholarly journals Factoring a group as an amalgamated free product

1973 ◽  
Vol 15 (2) ◽  
pp. 222-227 ◽  
Author(s):  
Edward T. Ordman
Keyword(s):  
Free Product ◽  
Proper Subgroup ◽  
Amalgamated Free Product ◽  
Image Position ◽  
The Cost

Even if in a decomposition of a group the Ai are completely indecomposable, there may be another decomposition with each Cj properly contained in some Ai a proper subgroup of B. The example of Bryce ([1], p. 636) may be modified, at the cost of having one Ai = B, so that I = J and Ci > Ai for all i. It is our object to study this relationship between decompositions of a group.

On the Combination Theorem for Negatively Curved Groups

1997 ◽  
Vol 07 (02) ◽  
pp. 267-276 ◽  
Author(s):  
Rita Gitik
Keyword(s):  
Free Product ◽  
Simple Proof ◽  
Sufficient Condition ◽  
Negatively Curved ◽  
Amalgamated Free Product

We give a simple proof of a sufficient condition for an amalgamated free product of two negatively curved groups to be negatively curved, and we compute the curvature of such products.

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