On exotic group C*-algebras
| Autor: | Zhong Jin Ruan, Matthew Wiersma |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Trace (linear algebra) Discrete group 010102 general mathematics Mathematics - Operator Algebras 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis Surjective function Factorization 0103 physical sciences FOS: Mathematics Order (group theory) 010307 mathematical physics Locally compact space 0101 mathematics Algebraic number Operator Algebras (math.OA) Analysis Quotient Mathematics |
| DOI: | 10.48550/arxiv.1505.00805 |
| Popis: | Let $\Gamma$ be a discrete group. A $C^*$-algebra $A$ is an exotic $C^*$-algebra (associated to $\Gamma$) if there exist proper surjective $C^*$-quotients $C^*(\Gamma)\to A\to C^*_r(\Gamma)$. In this paper, we show that a large class of exotic $C^*$-algebras have poor local properties. More precisely, we demonstrate the failure of local reflexitity, exactness, and local lifting property. Additionally, $A$ does not admit an amenable trace and, hence, is not quasidiagonal and does not have the WEP when $A$ is from the class of exotic $C^*$-algebras defined by Brown and Guentner. In order to achieve the main results of this paper, we prove a result which implies the factorization property for the class of discrete groups which are algebraic subgroups of locally compact amenable groups. Comment: Improvements to some proofs and several other changes, 14 pages, to appear in J. Funct. Anal |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|