论文标题
Sylvester等级的正常扩展功能
Sylvester rank functions for amenable normal extensions
论文作者
论文摘要
我们引入了具有有限的近似系统F的Unital环R的正常伸展s的概念，其中包括Gromov和Elek田地上的可木制代数，由Amenable组由扭曲的交叉产物，以及带有场扩展的张量。结果表明，s保留的每个sylvester矩阵级别rk都具有向Sylvester矩阵等级函数rk_f的规范扩展。对于S.在扭曲的交叉产物的情况下，张开的量和带有场扩展的张量产品，还表明RK_F依赖RK_F依赖RK持续。当一个可染色的组对保存奇特状态的Unital C*-代数具有扭曲的作用时，我们还表明，在奇怪状态构建的代数扭曲的交叉产物上，两个天然的Sylvester矩阵等级的功能是重合的。
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.
