AI 中文总结
该研究将Rokhlin G作用的分类推广到异常G作用情形，明确Kirchberg代数上带Rokhlin性质的G核的分类依据，还探究了相关K理论存在的障碍。
AI 中文摘要
给定一个有限群G，我们将Rokhlin G作用在C*-代数上的基本分类推广到具有Rokhlin性质的异常G作用的情形。对于分类计划所涵盖的C*-代数上的Rokhlin G核，这意味着在某些已知不变量上诱导的G作用决定了其共轭类。我们推广了Izumi的一个结果，证明了Kirchberg代数上具有Rokhlin性质的G核由其异常性以及K理论群上诱导的模结构所分类。我们探究了一般可分C*-代数上Rokhlin G核存在的K理论障碍，并利用这些障碍来刻画哪些G模结构可以作为具有给定提升障碍的、允许Rokhlin G核的Kirchberg代数的K群出现。
英文摘要
Given a finite group G, we develop a generalization of the fundamental classification of Rokhlin G-actions on C*-algebras to the setting of anomalous G-actions with the Rokhlin property. For Rokhlin G-kernels on C*-algebras covered by the classification program, this implies that the induced G-action on some known invariants determines the conjugacy class. Extending a result of Izumi, we show that G-kernels with the Rokhlin property on Kirchberg algebras are classified by their anomaly and the induced module structure on the K-theory groups. We explore K-theoretic obstructions for the existence of Rokhlin G-kernels on general separable C*-algebras and use these to characterise which G-module structures arise as K-groups of Kirchberg algebras admitting a Rokhlin G-kernel with a given lifting obstruction.
Comments42 pages
