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arXiv · 2002.12522

Sylvester rank functions for amenable normal extensions

Baojie Jiang·Hanfeng Li
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Abstract

We introduce a notion of amenable normal extension S of a unital ring R with a finite approximation system F, encompassing the amenable algebras over a field of Gromov and Elek, the twisted crossed product by an amenable group, and the tensor product with a field extension. It is shown that every Sylvester matrix rank function rk of R preserved by S has a canonical extension to a Sylvester matrix rank function rk_F for S. In the case of twisted crossed product by an amenable group, and the tensor product with a field extension, it is also shown that rk_F depends on rk continuously. When an amenable group has a twisted action on a unital C*-algebra preserving a tracial state, we also show that two natural Sylvester matrix rank functions on the algebraic twisted crossed product constructed out of the tracial state coincide.

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Baojie Jiang, Hanfeng Li. 2020-02-28. Sylvester rank functions for amenable normal extensions. https://doi.org/10.1016/j.jfa.2020.108913

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