The unique trace property of n-periodic product of groups

2017 ◽  
Vol 52 (4) ◽  
pp. 161-165
Author(s):  
V. S. Atabekyan ◽  
A. L. Gevorgyan ◽  
Sh. A. Stepanyan
Keyword(s):  
Unique Trace ◽  
Trace Property ◽  
Product Of Groups

scholarly journals C*-simplicity and the unique trace property for discrete groups

2017 ◽  
Vol 126 (1) ◽  
pp. 35-71 ◽  
Author(s):  
Emmanuel Breuillard ◽  
Mehrdad Kalantar ◽  
Matthew Kennedy ◽  
Narutaka Ozawa
Keyword(s):  
Discrete Groups ◽  
Unique Trace ◽  
Trace Property

scholarly journals Product of the GeneralizedL-Subgroups

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Dilek Bayrak ◽  
Sultan Yamak
Keyword(s):  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Product Of Groups

We introduce the notion of(λ,μ)-product ofL-subsets. We give a necessary and sufficient condition for(λ,μ)-L-subgroup of a product of groups to be(λ,μ)-product of(λ,μ)-L-subgroups.

A NOTE ON THE NORMS OF TRANSITION OPERATORS ON LAMPLIGHTER GRAPHS AND GROUPS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1261-1272 ◽  
Author(s):  
WOLFGANG WOESS
Keyword(s):  
Random Walk ◽  
Wreath Products ◽  
Locally Compact Group ◽  
Operator Matrix ◽  
Locally Compact ◽  
Finitely Generated Groups ◽  
Group Of Isometries ◽  
Transition Operators ◽  
Special Case ◽  
Product Of Groups

Let L≀X be a lamplighter graph, i.e., the graph-analogue of a wreath product of groups, and let P be the transition operator (matrix) of a random walk on that structure. We explain how methods developed by Saloff-Coste and the author can be applied for determining the ℓp-norms and spectral radii of P, if one has an amenable (not necessarily discrete or unimodular) locally compact group of isometries that acts transitively on L. This applies, in particular, to wreath products K≀G of finitely-generated groups, where K is amenable. As a special case, this comprises a result of Żuk regarding the ℓ2-spectral radius of symmetric random walks on such groups.

UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

2014 ◽  
Vol 79 (4) ◽  
pp. 1001-1019 ◽  
Author(s):  
ASHER M. KACH ◽  
ANTONIO MONTALBÁN
Keyword(s):  
Direct Product ◽  
Disjoint Union ◽  
Second Order ◽  
Linear Orders ◽  
Second Order Arithmetic ◽  
Order Arithmetic ◽  
Natural Classes ◽  
Product Of Groups

AbstractMany classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for some of these classes of structures, the resulting theory is bi-interpretable with second-order arithmetic.

scholarly journals Fundamental Group of Simple C*-algebras with Unique Trace III

2012 ◽  
Vol 64 (3) ◽  
pp. 573-587 ◽  
Author(s):  
Norio Nawata
Keyword(s):  
Fundamental Group ◽  
Lower Semicontinuous ◽  
Classification Theorem ◽  
Fundamental Groups ◽  
C Algebras ◽  
Scalar Multiple ◽  
Unique Trace ◽  
Densely Defined

Abstract We introduce the fundamental group ℱ(A) of a simple σ-inital C*-algebra A with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of Fundamental Group of Simple C*-algebras with Unique Trace I and II by Nawata andWatatani. Our definition in this paper makes sense for stably projectionless C*-algebras. We show that there exist separable stably projectionless C*-algebras such that their fundamental groups are equal to ℝ×+ by using the classification theorem of Razak and Tsang. This is a contrast to the unital case in Nawata and Watatani. This study is motivated by the work of Kishimoto and Kumjian.

INVARIANTS OF COLORED LINKS

1992 ◽  
Vol 01 (02) ◽  
pp. 161-184 ◽  
Author(s):  
YASUHIRO AKUTSU ◽  
TESTUO DEGUCHI ◽  
TOMOTADA OHTSUKI
Keyword(s):  
Braid Relation ◽  
Markov Trace ◽  
Trace Property

We define a new hierarchy of isotopy invariants of colored oriented links through oriented tangle diagrams. We prove the colored braid relation and the Markov trace property explicitly.

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