2015/05/04 by Ruan, Zhong-Jin, Wiersma, Matthew
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1505.00805
Let Γ be a discrete group. A C^*-algebra A is an exotic C^*-algebra (associated to Γ) if there exist proper surjective C^*-quotients C^*(Γ)→ A→ C^*r(Γ). 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.