论文标题
组和RFD财产的中央合并
Central amalgamation of groups and the RFD property
论文作者
论文摘要
这是一个古老而又具有挑战性的话题，要调查整个组C*-Algebra c*（g）的离散组是剩余的有限维度（RFD）。特别是，关于RFD属性在基本结构（例如合并的免费产品和HNN扩展）下的行为并不多。在[CS19]中，事实证明，实际上Abelian群体的中央合并免费产品是RFD。在本文中，我们证明这远远超出了这种情况。我们的方法基于显示从中央亚组引起的字符的某些近似属性。特别是，它使我们能够证明与有限生成的中央亚组合并的逐限制组的免费产品是RFD。另一方面，我们证明，在中央合并的免费产品下，RFD C*-Algebras（和组）的类别未关闭。也就是说，我们举例说明了RFD组（实际上是有限生成的RF组），其中央合并的免费产品不是RFD，此外，它甚至几乎没有最大周期性。这回答了可汗和莫里斯[KM82]的问题。
It is an old and challenging topic to investigate for which discrete groups G the full group C*-algebra C*(G) is residually finite-dimensional (RFD). In particular not much is known about how the RFD property behaves under fundamental constructions, such as amalgamated free products and HNN-extensions. In [CS19] it was proved that central amalgamated free products of virtually abelian groups are RFD. In this paper we prove that this holds much beyond this case. Our method is based on showing a certain approximation property for characters induced from central subgroups. In particular it allows us to prove that free products of polycyclic-by-finite groups amalgamated over finitely generated central subgroups are RFD. On the other hand we prove that the class of RFD C*-algebras (and groups) is not closed under central amalgamated free products. Namely we give an example of RFD groups (in fact finitely generated amenable RF groups) whose central amalgamated free product is not RFD, moreover it is not even maximally almost periodic. This answers a question of Khan and Morris [KM82].
