scholarly journals Hecke C*-Algebras, Schlichting Completions and Morita Equivalence

2008 ◽  
Vol 51 (3) ◽  
pp. 657-695 ◽  
Author(s):  
S. Kaliszewski ◽  
Magnus B. Landstad ◽  
John Quigg
Keyword(s):  
Normal Subgroup ◽  
Representation Theory ◽  
Direct Product ◽  
Open Subgroup ◽  
Hecke Algebra ◽  
Morita Equivalence ◽  
Compact Open Subgroup ◽  
C Algebras ◽  
Extended Analysis

AbstractThe Hecke algebra of a Hecke pair (G, H) is studied using the Schlichting completion (Ḡ, ), which is a Hecke pair whose Hecke algebra is isomorphic to and which is topologized so that is a compact open subgroup of Ḡ. In particular, the representation theory and C*-completions of are addressed in terms of the projection using both Fell's and Rieffel's imprimitivity theorems and the identity . An extended analysis of the case where H is contained in a normal subgroup of G (and in particular the case where G is a semi-direct product) is carried out, and several specific examples are analysed using this approach.

scholarly journals Homomorphisms into totally disconnected, locally compact groups with dense image

2019 ◽  
Vol 31 (3) ◽  
pp. 685-701 ◽  
Author(s):  
Colin D. Reid ◽  
Phillip R. Wesolek
Keyword(s):  
Normal Subgroup ◽  
Open Subgroup ◽  
Locally Compact Groups ◽  
Group Homomorphism ◽  
Compact Groups ◽  
Locally Compact ◽  
Compact Open Subgroup ◽  
Dense Image ◽  
Profinite Completions ◽  
Totally Disconnected

Abstract Let {\phi:G\rightarrow H} be a group homomorphism such that H is a totally disconnected locally compact (t.d.l.c.) group and the image of ϕ is dense. We show that all such homomorphisms arise as completions of G with respect to uniformities of a particular kind. Moreover, H is determined up to a compact normal subgroup by the pair {(G,\phi^{-1}(L))} , where L is a compact open subgroup of H. These results generalize the well-known properties of profinite completions to the locally compact setting.

scholarly journals Hecke C*-algebras and semi-direct products

2009 ◽  
Vol 52 (1) ◽  
pp. 127-153 ◽  
Author(s):  
S. Kaliszewski ◽  
Magnus B. Landstad ◽  
John Quigg
Keyword(s):  
Fixed Point ◽  
Direct Product ◽  
Hecke Algebra ◽  
Quadratic Extension ◽  
Crossed Product ◽  
Direct Products ◽  
C Algebras ◽  
Fixed Point Algebra

AbstractWe analyse Hecke pairs (G,H) and the associated Hecke algebra $\mathcal{H}$ when G is a semi-direct product N ⋊ Q and H = M ⋊ R for subgroups M ⊂ N and R ⊂ Q with M normal in N. Our main result shows that, when (G,H) coincides with its Schlichting completion and R is normal in Q, the closure of $\mathcal{H}$ in C*(G) is Morita–Rieffel equivalent to a crossed product I⋊βQ/R, where I is a certain ideal in the fixed-point algebra C*(N)R. Several concrete examples are given illustrating and applying our techniques, including some involving subgroups of GL(2,K) acting on K2, where K = ℚ or K = ℤ[p−1]. In particular we look at the ax + b group of a quadratic extension of K.

C*-algebras of Clifford semigroups

1989 ◽  
Vol 111 (1-2) ◽  
pp. 129-145 ◽  
Author(s):  
John Duncan ◽  
A.L.T. Paterson
Keyword(s):  
Representation Theory ◽  
Clifford Semigroup ◽  
Sheaf Theory ◽  
C Algebras ◽  
Clifford Semigroups

SynopsisWe investigate algebras associated with a (discrete) Clifford semigroup S =∪ {Ge: e ∈ E{. We show that the representation theory for S is determined by an enveloping Clifford semigroup UC(S) =∪ {Gx: x ∈ X} where X is the filter completion of the semilattice E. We describe the representation theory in terms of both disintegration theory and sheaf theory.

scholarly journals HILBERT C*-BIMODULES OF FINITE INDEX AND APPROXIMATION PROPERTIES OF C*-ALGEBRAS

2017 ◽  
Vol 60 (2) ◽  
pp. 321-331
Author(s):  
MARZIEH FOROUGH ◽  
MASSOUD AMINI
Keyword(s):  
Finite Index ◽  
Morita Equivalence ◽  
Discrete Groups ◽  
Crossed Products ◽  
Approximation Properties ◽  
C Algebras ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
The Stability

AbstractLet A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

scholarly journals MORITA EQUIVALENCE FOR C*-ALGEBRAS WITH THE WEAK BANACH–SAKS PROPERTY. II

2007 ◽  
Vol 50 (1) ◽  
pp. 185-195
Author(s):  
Masaharu Kusuda
Keyword(s):  
Morita Equivalence ◽  
C Algebras ◽  
Morita Equivalent ◽  
Finite Dimensional

AbstractLet $C^*$-algebras $A$ and $B$ be Morita equivalent and let $X$ be an $A$–$B$-imprimitivity bimodule. Suppose that $A$ or $B$ is unital. It is shown that $X$ has the weak Banach–Saks property if and only if it has the uniform weak Banach–Saks property. Thus, we conclude that $A$ or $B$ has the weak Banach–Saks property if and only if $X$ does so. Furthermore, when $C^*$-algebras $A$ and $B$ are unital, it is shown that $X$ has the Banach–Saks property if and only if it is finite dimensional.

Sign in / Sign up

Export Citation Format

Share Document