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.

scholarly journals A Short Note on the Continuous Rokhlin Property and the Universal Coefficient Theorem in E-theory

2015 ◽  
Vol 58 (2) ◽  
pp. 374-380 ◽  
Author(s):  
Gábor Szabó
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Short Note ◽  
Circle Actions ◽  
Continuous Action ◽  
C Algebra ◽  
C Algebras ◽  
Group A ◽  
Fixed Point Algebra ◽  
Universal Coefficient Theorem

AbstractLet G be a metrizable compact group, A a separable C*-algebra, and α:G → Aut(A) a strongly continuous action. Provided that α satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in E-theory passes from Ato the crossed product C*-algebra A⋊α G and the ûxed point algebra Aα. This extends a similar result by Gardella for KK-theory in the case of unital C*-algebras but with a shorter and less technical proof. For circle actions on separable unital C*-algebras with the continuous Rokhlin property, we establish a connection between the Etheory equivalence class of A and that of its fixed point algebra Aα.

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

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.

The left Hilbert algebra associated to a semi-direct product

1977 ◽  
Vol 82 (3) ◽  
pp. 411-418 ◽  
Author(s):  
R. Rousseau
Keyword(s):  
Direct Product ◽  
Compact Support ◽  
Continuous Functions ◽  
Crossed Product ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Hilbert Algebra ◽  
Locally Compact ◽  
Continuous Action ◽  
Canonical Weight

AbstractLet A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".

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.

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