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Residual finiteness for central pushouts
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-23 , DOI: 10.1090/proc/15368 Alexandru Chirvasitu
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-23 , DOI: 10.1090/proc/15368 Alexandru Chirvasitu
Abstract:We prove that pushouts 
of residually finite-dimensional (RFD) 
-algebras over central subalgebras are always residually finite-dimensional provided the fibers 
and 
, 
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 
-algebras. Along the way, we discuss the problem of when, given a central group embedding 
, the resulting 
-algebra morphism is a continuous field: this is always the case for amenable 
but not in general.
中文翻译：
中央推出物的剩余有限性
摘要：我们证明了pushouts的残余有限维（RFD）-代数超过中央子代数总是残余有限维提供的纤维和，是RFD，回收和概括由柯察金及考特尼-舒尔曼结果。然后，这可以使我们证明，可满足组的某些中心推出项目具有RFD组-代数。在此过程中，我们讨论了以下问题：在给定一个中心组嵌入的情况下，所产生的-代数态射影是一个连续的字段：总是可以接受的，但总的来说并非如此。
更新日期：2021-04-22
of residually finite-dimensional (RFD) -algebras over central subalgebras are always residually finite-dimensional provided the fibers and , 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 -algebras. Along the way, we discuss the problem of when, given a central group embedding , the resulting -algebra morphism is a continuous field: this is always the case for amenable but not in general. 中文翻译：
中央推出物的剩余有限性
摘要：我们证明了pushouts
的残余有限维（RFD）-代数超过中央子代数总是残余有限维提供的纤维和，是RFD，回收和概括由柯察金及考特尼-舒尔曼结果。然后，这可以使我们证明，可满足组的某些中心推出项目具有RFD组-代数。在此过程中，我们讨论了以下问题：在给定一个中心组嵌入的情况下，所产生的-代数态射影是一个连续的字段：总是可以接受的，但总的来说并非如此。 
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