scholarly journals The Tracial Class Property for Crossed Products by Finite Group Actions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xinbing Yang ◽  
Xiaochun Fang
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Crossed Products ◽  
Finite Group Actions ◽  
Infinite Dimensional ◽  
A Finite Group ◽  
Tracial Rokhlin Property

We define the concept of tracial𝒞-algebra ofC*-algebras, which generalize the concept of local𝒞-algebra ofC*-algebras given by H. Osaka and N. C. Phillips. Let𝒞be any class of separable unitalC*-algebras. LetAbe an infinite dimensional simple unital tracial𝒞-algebra with the (SP)-property, and letα:G→Aut(A)be an action of a finite groupGonAwhich has the tracial Rokhlin property. ThenA  ×α  Gis a simple unital tracial𝒞-algebra.

Certain properties for crossed products by automorphisms with a certain non-simple tracial Rokhlin property

2012 ◽  
Vol 33 (5) ◽  
pp. 1391-1400 ◽  
Author(s):  
XIAOCHUN FANG ◽  
QINGZHAI FAN
Keyword(s):  
Finite Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Infinite Dimensional ◽  
Crossed Product Algebra ◽  
A Finite Group ◽  
Product Algebra ◽  
Tracial Rokhlin Property

AbstractLet $\Omega $ be a class of unital $C^*$-algebras. Then any simple unital $C^*$-algebra $A\in \mathrm {TA}(\mathrm {TA}\Omega )$ is a $\mathrm {TA}\Omega $ algebra. Let $A\in \mathrm {TA}\Omega $ be an infinite-dimensional $\alpha $-simple unital $C^*$-algebra with the property SP. Suppose that $\alpha :G\to \mathrm {Aut}(A)$ is an action of a finite group $G$ on $A$ which has a certain non-simple tracial Rokhlin property. Then the crossed product algebra $C^*(G,A,\alpha )$ belongs to $\mathrm {TA}\Omega $.

scholarly journals Crossed products by finite group actions with the Rokhlin property

2011 ◽  
Vol 270 (1-2) ◽  
pp. 19-42 ◽  
Author(s):  
Hiroyuki Osaka ◽  
N. Christopher Phillips
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Crossed Products ◽  
Finite Group Actions

Extending finite group actions on surfaces to hyperbolic 3-manifolds

1995 ◽  
Vol 117 (1) ◽  
pp. 137-151 ◽  
Author(s):  
Monique Gradolato ◽  
Bruno Zimmermann
Keyword(s):  
Finite Group ◽  
Riemann Surface ◽  
Finite Groups ◽  
Group Actions ◽  
Geodesic Boundary ◽  
Totally Geodesic ◽  
Finite Group Actions ◽  
Closed Riemann Surface ◽  
A Finite Group ◽  
The Given

Let G be a finite group of orientation preserving isometrics of a closed orientable hyperbolic 2-manifold Fg of genus g > 1 (or equivalently, a finite group of conformal automorphisms of a closed Riemann surface). We say that the G-action on Fgbounds a hyperbolic 3-manifold M if M is a compact orientable hyperbolic 3-manifold with totally geodesic boundary Fg (as the only boundary component) such that the G-action on Fg extends to a G-action on M by isometrics. Symmetrically we will also say that the 3-manifold M bounds the given G-action. We are especially interested in Hurwitz actions, i.e. finite group actions on surfaces of maximal possible order 84(g — 1); the corresponding finite groups are called Hurwitz groups. First examples of bounding and non-bounding Hurwitz actions were given in [16].

scholarly journals Conjugacy of free finite group actions on infranilmanifolds

1990 ◽  
Vol 32 (2) ◽  
pp. 239-240 ◽  
Author(s):  
Michał Sadowski
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Finite Group Actions ◽  
Affine Action ◽  
A Finite Group ◽  
Free Actions

In this note we give the proof of the following result (previously known for homotopically trivial and free actions on infranilmanifolds [3, Theorem 5.6]).Theorem 1. Let G be a finite group acting freely and smoothly on a closed infranilmanifold M. Assume that dim M≠3, 4. Then the action of G is topologically conjugate to an affine action.

Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions

1986 ◽  
Vol 29 (3) ◽  
pp. 274-280 ◽  
Author(s):  
Piotr Grzeszczuk ◽  
Edmund R. Puczyłowski
Keyword(s):  
Finite Group ◽  
Fixed Points ◽  
Modular Lattice ◽  
Group Actions ◽  
Modular Lattices ◽  
Finite Group Actions ◽  
Chain Conditions ◽  
Goldie Dimension ◽  
A Finite Group

AbstractA relation between Goldie dimensions of a modular lattice L and its sublattice LG of fixed points under a finite group G of automorphisms of L is obtained. The method used also gives a relation between ACC (DCC) for L and for LG. The results obtained are applied to rings and modules.

scholarly journals Finite group actions on 4-manifolds

1999 ◽  
Vol 66 (3) ◽  
pp. 287-296 ◽  
Author(s):  
Yong Seung Cho
Keyword(s):  
Finite Group ◽  
Fundamental Group ◽  
Group Actions ◽  
Witten Invariant ◽  
Finite Group Actions ◽  
Finite Fundamental Group ◽  
A Finite Group

AbstractLet X be a closed, oriented, smooth 4-manifold with a finite fundamental group and with a non-vanishing Seiberg-Witten invariant. Let G be a finite group. If G acts smoothly and freely on X, then the quotient X/G cannot be decomposed as X1#X2 with (Xi) > 0, i = 1, 2. In addition let X be symplectic and c1(X)2 > 0 and b+2(X) > 3. If σ is a free anti-symplectic involution on X then the Seiberg-Witten invariants on X/σ vanish for all spinc structures on X/σ, and if η is a free symplectic involution on X then the quotients X/σ and X/η are not diffeomorphic to each other.

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