The $$C^*$$-algebra of the semi-direct product $$K < imes A$$

2020 ◽  
Vol 192 (4) ◽  
pp. 915-934
Author(s):  
Hedi Regeiba ◽  
Jean Ludwig
Keyword(s):  
Direct Product ◽  
C Algebra

scholarly journals A Computation with the Connes–Thom Isomorphism

2015 ◽  
Vol 58 (4) ◽  
pp. 846-857
Author(s):  
S. Sundar
Keyword(s):  
Direct Product ◽  
Invertible Matrix ◽  
Left Multiplication ◽  
Continuous Action ◽  
C Algebra ◽  
Dilation Matrix ◽  
Thom Isomorphism

AbstractLet A ∊ Mn(ℝ) be an invertible matrix. Consider the semi-direct product ℝn ⋊ ℤ where the action of ℤ on ℝn is induced by the left multiplication by A. Let (α, τ) be a strongly continuous action of ℝn ⋊ ℤ on a C*-algebra B where α is a strongly continuous action of ℝn and τ is an automorphism. The map τ induces a map . We show that, at the K-theory level, τ commutes with the Connes–Thom map if det(A) > 0 and anticommutes if det(A) < 0. As an application, we recompute the K-groups of the Cuntz–Li algebra associated with an integer dilation matrix.

TOPOLOGICAL K-THEORY OF THE GROUP C*-ALGEBRA OF A SEMI-DIRECT PRODUCT ℤn ⋊ ℤ/m FOR A FREE CONJUGATION ACTION

2012 ◽  
Vol 04 (02) ◽  
pp. 121-172 ◽  
Author(s):  
MARTIN LANGER ◽  
WOLFGANG LÜCK
Keyword(s):  
Direct Product ◽  
Group Extension ◽  
C Algebra ◽  
K Theory

We compute the topological K-theory of the group C*-algebra [Formula: see text] for a group extension 1 → ℤn → Γ → ℤ/m → 1 provided that the conjugation action of ℤ/m on ℤn is free outside the origin.

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

On the g-hypergroupoids associated with g-hypergraphs

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4819-4831 ◽  
Author(s):  
Mehdi Farshi ◽  
Bijan Davvaz ◽  
Saeed Mirvakili
Keyword(s):  
Direct Product ◽  
Fundamental Relation ◽  
Join Space ◽  
Commutative Hypergroup ◽  
Regular Relation

In this paper, we associate a partial g-hypergroupoid with a given g-hypergraph and analyze the properties of this hyperstructure. We prove that a g-hypergroupoid may be a commutative hypergroup without being a join space. Next, we define diagonal direct product of g-hypergroupoids. Further, we construct a sequence of g-hypergroupoids and investigate some relationships between it?s terms. Also, we study the quotient of a g-hypergroupoid by defining a regular relation. Finally, we describe fundamental relation of an Hv-semigroup as a g-hypergroupoid.

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 On the sandpile model of modified wheels II

2020 ◽  
Vol 18 (1) ◽  
pp. 1531-1539
Author(s):  
Zahid Raza ◽  
Mohammed M. M. Jaradat ◽  
Mohammed S. Bataineh ◽  
Faiz Ullah
Keyword(s):  
Direct Product ◽  
Critical Group ◽  
Complete Structure ◽  
Sandpile Model ◽  
Cyclic Subgroups ◽  
Algebr Comb ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
Sandpile Group

Abstract We investigate the abelian sandpile group on modified wheels {\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on {\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on {\hat{W}}_{n} is the direct product of two cyclic subgroups of order {a}_{n} and 3{a}_{n} for n even and of order {a}_{n} and 2{a}_{n} for n odd, respectively.

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