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arXiv · 2211.07397

Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property

Haotian Tian·Xiaochun Fang
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Abstract

In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its original algebra: (1) stable rank one; (2) real rank zero; (3) $\beta$-comparison; (4) Winter's $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible.

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Haotian Tian, Xiaochun Fang. 2022-11-11. Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property. https://doi.org/10.1216/rmj.2025.55.847

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