Voiculescu定理，Sobolev引理和光滑代数的扩张
Voiculescu theorem, Sobolev lemma, and extensions of smooth algebras
摘要：
对任意Fréchet算子理想$\Cal K_τ$，给出了非交换光滑代数范畴上统一的B-D-F扩张函子$\operatorname{Ext}_τ$的解析基础.结合Arveson和Voiculescu设计的技术，我们推广Voiculescu定理光滑代数和Fréchet算子理想。其中的一个关键概念是$τ$ -光滑性，通过非交换的Sobolev引理，证明了光滑函数代数的$τ$ -光滑性.对于许多示例，计算组$\operatorname{Ext}_τ$。
英文摘要：
We present the analytic foundation of a unified B-D-F extension functor $\operatorname{Ext}_τ$ on the category of noncommutative smooth algebras, for any Fréchet operator ideal $\Cal K_τ$. Combining the techniques devised by Arveson and Voiculescu, we generalize Voiculescu's theorem to smooth algebras and Fréchet operator ideals. A key notion involved is $τ$-smoothness, which is verified for the algebras of smooth functions, via a noncommutative Sobolev lemma. The groups $\operatorname{Ext}_τ$ are computed for many examples.
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