论文标题
中央定位的残留有限
Residual finiteness for central pushouts
论文作者
论文摘要
我们证明，在中央亚级别的剩余有限维（RFD）$ c^*$ - 代数$ a*_cb $的下降$ a*_cb $，只要纤维$ a_p $ and $ b_p $和$ b_p $，$ p \，$ p \ in \ mathrm {spec} 〜c $ rfd，rfd rfd rfd and recounce and shercne and or rfd ands shercne和corman shecn and or grense and or rfd，然后，这使我们能够证明某些Amenable小组的中央下调具有RFD组$ C^*$ - 代数。在此过程中，我们讨论了一个何时嵌入$ h \ le g $的中央组，结果$ c^*$ - 代数形态是一个连续的领域：对于不符合的$ g $，但总体而言并非如此。
We prove that pushouts $A*_CB$ of residually finite-dimensional (RFD) $C^*$-algebras over central subalgebras are always residually finite-dimensional provided the fibers $A_p$ and $B_p$, $p\in \mathrm{spec}~C$ are RFD, recovering and generalizing results by Korchagin and Courtney-Shulman. This then allows us to prove that certain central pushouts of amenable groups have RFD group $C^*$-algebras. Along the way, we discuss the problem of when, given a central group embedding $H\le G$, the resulting $C^*$-algebra morphism is a continuous field: this is always the case for amenable $G$ but not in general.
