HAAGERUP PROPERTY FOR C*-CROSSED PRODUCTS

作者：Meng, Qing^*

来源：Bulletin of the Australian Mathematical Society, 2017, 95(1): 144-148.

DOI：10.1017/S0004972716000642

• C*-algebra
• Haagerup property
• tracial state
• crossed product

Let Gamma be a countable discrete group that acts on a unital C*-algebra A through an action alpha. If A has a faithful alpha-invariant tracial state tau, then tau' =tau circle epsilon is a faithful tracial state of A proportional to(alpha,r) Gamma where epsilon : A proportional to(alpha,r) Gamma -> A is the canonical faithful conditional expectation. We show that (A proportional to(alpha,r) Gamma,tau') has the Haagerup property if and only if both (A,tau) and Gamma have the Haagerup property. As a consequence, suppose that (A proportional to(alpha,r) Gamma,tau') has the Haagerup property where has property T and A has strong property T. Then Gamma is finite and A is residually finite-dimensional.

• 出版日期2017-2
• 单位南开大学