scholarly journals The general Ikehata theorem forH-separable crossed products

2000 ◽  
Vol 23 (10) ◽  
pp. 657-662
Author(s):  
George Szeto ◽  
Lianyong Xue
Keyword(s):  
Automorphism Group ◽  
Galois Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Separable Extension ◽  
Factor Set ◽  
Commutative Subring

LetBbe a ring with1,   Cthe center ofB,   Gan automorphism group ofBof ordernfor some integern,   CGthe set of elements inCfixed underG,   Δ=Δ(B,G,f)a crossed product overBwherefis a factor set fromG×GtoU(CG). It is shown thatΔis anH-separable extension ofBandVΔ(B)is a commutative subring ofΔif and only ifCis a Galois algebra overCGwith Galois groupG|C≅G.

scholarly journals Crossed Products and Ramification

1966 ◽  
Vol 28 ◽  
pp. 85-111 ◽  
Author(s):  
Susan Williamson
Keyword(s):  
Galois Group ◽  
Galois Extension ◽  
Valuation Ring ◽  
Field Extension ◽  
Integral Closure ◽  
Crossed Product ◽  
Crossed Products ◽  
Quotient Field ◽  
Rank One ◽  
Definition Of

Introduction. Let S be the integral closure of a complete discrete rank one valuation ring R in a finite Galois extension of the quotient field of R, and let G denote the Galois group of the quotient field extension. Auslander and Rim have shown in [3] that the trivial crossed product Δ (1, S, G) is an hereditary order if and only if 5 is a tamely ramified extension of R. And the author has proved in [7] that if the extension S of R is tamely ramified then the crossed product Δ(f, 5, G) is a Π-principal hereditary order for each 2-cocycle f in Z2(G, U(S)). (See Section 1 for the definition of Π-principal hereditary order.) However, the author has exhibited in [8] an example of a crossed product Δ(f, S, G) which is a Π-principal hereditary order in the case when S is a wildly ramified extension of R.

scholarly journals On a Crossed Product of a Division Ring

1969 ◽  
Vol 35 ◽  
pp. 47-51 ◽  
Author(s):  
Nobuo Nobusawa
Keyword(s):  
Automorphism Group ◽  
Division Ring ◽  
Crossed Product ◽  
Regular Elements ◽  
Factor Set

1. Let R and C be a ring and its center, and G an automorphism group of R of order n. By a factor set {cα,τ}, we mean a system of regular elements cα,τ (α,τ ∈ G) in C such that(1)

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

scholarly journals A rigidity result for crossed products of actions of Baumslag–Solitar groups

2015 ◽  
Vol 26 (14) ◽  
pp. 1550117
Author(s):  
Niels Meesschaert
Keyword(s):  
Probability Measure ◽  
Free Probability ◽  
Crossed Product ◽  
Crossed Products ◽  
Orbit Equivalence ◽  
Rigidity Result ◽  
Profinite Completions ◽  
Abelian Subgroups ◽  
Measure Equivalence ◽  
Measure Preserving Actions

Let [Formula: see text] and [Formula: see text] be two ergodic essentially free probability measure preserving actions of nonamenable Baumslag–Solitar groups whose canonical almost normal abelian subgroups act aperiodically. We prove that an isomorphism between the corresponding crossed product II1 factors forces [Formula: see text] when [Formula: see text] and [Formula: see text] when [Formula: see text]. This improves an orbit equivalence rigidity result obtained by Houdayer and Raum in [Baumslag–Solitar groups, relative profinite completions and measure equivalence rigidity, J. Topol. 8 (2015) 295–313].

Morita equivalences between fixed point algebras and crossed products

1999 ◽  
Vol 125 (1) ◽  
pp. 43-52 ◽  
Author(s):  
CHI-KEUNG NG
Keyword(s):  
Fixed Point ◽  
Quantum Group ◽  
Type Theorem ◽  
Compact Quantum Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Morita Equivalent ◽  
Fixed Point Algebra

In this paper, we will prove that if A is a C*-algebra with an effective coaction ε by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an imprimitivity type theorem for crossed products of coactions by discrete Kac C*-algebras.

scholarly journals On separable noncyclic extensions of rings

1983 ◽  
Vol 34 (3) ◽  
pp. 394-398 ◽  
Author(s):  
George Szeto ◽  
Yuen-Fat Wong
Keyword(s):  
Cyclic Extension ◽  
Crossed Product ◽  
Special Factor ◽  
Factor Set

AbstractThe separable cyclic extension of rings is generalized to a separable noncyclic extension of rings: a crossed product with a factor set over a ring (not necessarily commutative). A representation of separable idempotents for a separable crossed product is obtained, and simplifications for some special factor sets are also given.

scholarly journals Coarse quotients by group actions and the maximal Roe algebra

2019 ◽  
Vol 11 (04) ◽  
pp. 875-907
Author(s):  
Logan Higginbotham ◽  
Thomas Weighill
Keyword(s):  
Automorphism Group ◽  
Metric Space ◽  
Large Scale ◽  
Countable Group ◽  
Crossed Product ◽  
Property A ◽  
Bounded Geometry ◽  
Roe Algebra ◽  
Scale Spaces ◽  
The Ideal

For a finitely generated group [Formula: see text] acting on a metric space [Formula: see text], Roe defined the warped space [Formula: see text], which one can view as a kind of large scale quotient of [Formula: see text] by the action of [Formula: see text]. In this paper, we generalize this notion to the setting of actions of arbitrary groups on large scale spaces. We then restrict our attention to what we call coarsely discontinuous actions by coarse equivalences and show that for such actions the group [Formula: see text] can be recovered as an appropriately defined automorphism group [Formula: see text] when [Formula: see text] satisfies a large scale connectedness condition. We show that for a coarsely discontinuous action of a countable group [Formula: see text] on a discrete bounded geometry metric space [Formula: see text] there is a relation between the maximal Roe algebras of [Formula: see text] and [Formula: see text], namely that there is a ∗-isomorphism [Formula: see text], where [Formula: see text] is the ideal of compact operators. If [Formula: see text] has Property A and [Formula: see text] is amenable, then [Formula: see text] has Property A, and thus the maximal Roe algebra and full crossed product can be replaced by the usual Roe algebra and reduced crossed product respectively in the above equation.

scholarly journals Extension problems and non-Abelian duality for C*-algebras

2007 ◽  
Vol 75 (2) ◽  
pp. 229-238 ◽  
Author(s):  
Astrid an Huef ◽  
S. Kaliszewski ◽  
Iain Raeburn
Keyword(s):  
Compact Group ◽  
Unitary Representation ◽  
Closed Subgroup ◽  
Locally Compact Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Test Question ◽  
Locally Compact ◽  
Dual Representation ◽  
C Algebras

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

scholarly journals Discrete product systems with twisted units

1995 ◽  
Vol 52 (2) ◽  
pp. 317-326 ◽  
Author(s):  
Marcelo Laca
Keyword(s):  
Dynamical System ◽  
Crossed Product ◽  
Type I ◽  
Crossed Products ◽  
Product System ◽  
C Algebra ◽  
Covariant Representations ◽  
Product Systems ◽  
Recent Theorem ◽  
I Factor

The spectral C*-algebra of the discrete product systems of H.T. Dinh is shown to be a twisted semigroup crossed product whenever the product system has a twisted unit. The covariant representations of the corresponding dynamical system are always faithful, implying the simplicity of these crossed products; an application of a recent theorem of G.J. Murphy gives their nuclearity. Furthermore, a semigroup of endomorphisms of B(H) having an intertwining projective semigroup of isometries can be extended to a group of automorphisms of a larger Type I factor.

scholarly journals Almost Finiteness for General Étale Groupoids and Its Applications to Stable Rank of Crossed Products

2018 ◽  
Vol 2020 (19) ◽  
pp. 6007-6041 ◽  
Author(s):  
Yuhei Suzuki
Keyword(s):  
Amenable Group ◽  
Cantor Set ◽  
Stable Rank ◽  
Crossed Product ◽  
Local Version ◽  
Crossed Products ◽  
Subexponential Growth ◽  
Minimal Action ◽  
New Strategy ◽  
Totally Disconnected

Abstract We extend Matui’s notion of almost finiteness to general étale groupoids and show that the reduced groupoid C$^{\ast }$-algebras of minimal almost finite groupoids have stable rank 1. The proof follows a new strategy, which can be regarded as a local version of the large subalgebra argument. The following three are the main consequences of our result: (1) for any group of (local) subexponential growth and for any its minimal action admitting a totally disconnected free factor, the crossed product has stable rank 1; (2) any countable amenable group admits a minimal action on the Cantor set, all whose minimal extensions form the crossed product of stable rank 1; and (3) for any amenable group, the crossed product of the universal minimal action has stable rank 1.

Sign in / Sign up

Export Citation Format

Share Document