scholarly journals K- and L-theory of graph products of groups

2021 ◽  
Vol 15 (1) ◽  
pp. 269-311
Author(s):  
Daniel Kasprowski ◽  
Kevin Li ◽  
Wolfgang Lück
Keyword(s):  
Graph Products ◽  
Products Of Groups

Graph products of groups and group spaces

1995 ◽  
Vol 53 (1-2) ◽  
pp. 131-147 ◽  
Author(s):  
Jochen Pfalzgraf
Keyword(s):  
Graph Products ◽  
Products Of Groups

scholarly journals The Identity Problem for Graph Products of Groups

1993 ◽  
Vol 162 (1) ◽  
pp. 168-177 ◽  
Author(s):  
Y.G. Baik ◽  
J. Howie ◽  
S.J. Pride
Keyword(s):  
Graph Products ◽  
Identity Problem ◽  
Products Of Groups

ORDERING GRAPH PRODUCTS OF GROUPS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250037 ◽  
Author(s):  
I. M. CHISWELL
Keyword(s):  
Graph Products ◽  
Graph Product ◽  
Free Products ◽  
Products Of Groups

It is shown that a graph product of right-orderable groups is right orderable, and that a graph product of (two-sided) orderable groups is orderable. The latter result makes use of a new way of ordering free products of groups.

scholarly journals Automorphisms of graph products of groups from a geometric perspective

2019 ◽  
Vol 119 (6) ◽  
pp. 1745-1779 ◽  
Author(s):  
Anthony Genevois ◽  
Alexandre Martin
Keyword(s):  
Graph Products ◽  
Products Of Groups

On graph products of multipliers and the Haagerup property for -dynamical systems

2019 ◽  
Vol 40 (12) ◽  
pp. 3188-3216
Author(s):  
SCOTT ATKINSON
Keyword(s):  
Dynamical Systems ◽  
Positive Definite ◽  
Alternative Proof ◽  
Discrete Groups ◽  
Graph Products ◽  
Graph Product ◽  
Haagerup Property ◽  
Products Of Groups ◽  
Product Action

We consider the notion of the graph product of actions of discrete groups $\{G_{v}\}$ on a $C^{\ast }$-algebra ${\mathcal{A}}$ and show that under suitable commutativity conditions the graph product action $\star _{\unicode[STIX]{x1D6E4}}\unicode[STIX]{x1D6FC}_{v}:\star _{\unicode[STIX]{x1D6E4}}G_{v}\curvearrowright {\mathcal{A}}$ has the Haagerup property if each action $\unicode[STIX]{x1D6FC}_{v}:G_{v}\curvearrowright {\mathcal{A}}$ possesses the Haagerup property. This generalizes the known results on graph products of groups with the Haagerup property. To accomplish this, we introduce the graph product of multipliers associated to the actions and show that the graph product of positive-definite multipliers is positive definite. These results have impacts on left-transformation groupoids and give an alternative proof of a known result for coarse embeddability. We also record a cohomological characterization of the Haagerup property for group actions.

scholarly journals Noncommutative network models

2019 ◽  
Vol 30 (1) ◽  
pp. 14-32
Author(s):  
Joe Moeller
Keyword(s):  
Complex Networks ◽  
Network Model ◽  
Network Models ◽  
Graph Products ◽  
Bounded Degree ◽  
Simple Graphs ◽  
Products Of Groups ◽  
Free Network ◽  
Model Networks

AbstractNetwork models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between all edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct the free network model on a given monoid, which can model networks with bounded degree. To do this, we generalize Green’s graph products of groups to pointed categories which are finitely complete and cocomplete.

scholarly journals Separability properties of automorphisms of graph products of groups

2016 ◽  
Vol 26 (01) ◽  
pp. 1-27
Author(s):  
Michal Ferov
Keyword(s):  
Finite Groups ◽  
Nilpotent Groups ◽  
Technical Condition ◽  
Graph Products ◽  
Graph Product ◽  
Finitely Generated ◽  
Residually Finite ◽  
Products Of Groups ◽  
Text Version ◽  
Inner Automorphisms

We study properties of automorphisms of graph products of groups. We show that graph product [Formula: see text] has nontrivial pointwise inner automorphisms if and only if some vertex group corresponding to a central vertex has nontrivial pointwise inner automorphisms. We use this result to study residual finiteness of [Formula: see text]. We show that if all vertex groups are finitely generated residually finite and the vertex groups corresponding to central vertices satisfy certain technical (yet natural) condition, then [Formula: see text] is residually finite. Finally, we generalize this result to graph products of residually [Formula: see text]-finite groups to show that if [Formula: see text] is a graph product of finitely generated residually [Formula: see text]-finite groups such that the vertex groups corresponding to central vertices satisfy the [Formula: see text]-version of the technical condition then [Formula: see text] is virtually residually [Formula: see text]-finite. We use this result to prove bi-orderability of Torreli groups of some graph products of finitely generated residually torsion-free nilpotent groups.

scholarly journals Rigidity of graph products of groups

2003 ◽  
Vol 3 (2) ◽  
pp. 1079-1088 ◽  
Author(s):  
David G Radcliffe
Keyword(s):  
Graph Products ◽  
Products Of Groups
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