论文标题
扭曲类动力学系统的HAAGERUP属性
The Haagerup property for twisted groupoid dynamical systems
论文作者
论文摘要
我们介绍了自然定义的正定运算符值乘数，用于扭曲的groupoid $ c^*$ - 动态系统的Haagerup属性。通过开发“ haagerup技巧”的版本，我们证明了该属性等于减少的交叉产品$ c^*$ - 代数相对于规范的条件期望$ e $。这扩展了Dong and Ruan的定理，以进行离散的群体行动，并意味着，当且仅当相关的Weylsoid具有TU的意义时，给定的cartan包含$ C^*$ - 代数具有Haagerup属性。我们使用后一个语句来证明，每个可分离的$ c^*$ - 代数，具有haagerup属性相对于某些cartan subsalgebra满足通用系数定理。这概括了Barlak和Li对UCT的核琴琴对的最新结果。
We introduce the Haagerup property for twisted groupoid $C^*$-dynamical systems in terms of naturally defined positive-definite operator-valued multipliers. By developing a version of `the Haagerup trick' we prove that this property is equivalent to the Haagerup property of the reduced crossed product $C^*$-algebra with respect to the canonical conditional expectation $E$. This extends a theorem of Dong and Ruan for discrete group actions, and implies that a given Cartan inclusion of separable $C^*$-algebras has the Haagerup property if and only if the associated Weyl groupoid has the Haagerup property in the sense of Tu. We use the latter statement to prove that every separable $C^*$-algebra which has the Haagerup property with respect to some Cartan subalgebra satisfies the Universal Coefficient Theorem. This generalises a recent result of Barlak and Li on the UCT for nuclear Cartan pairs.
