具有局部提升性质的泛$C^ * $代数

Pub Date : 2021-08-31 DOI:10.7146/math.scand.a-126018

Kristin Courtney

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引用次数: 7

摘要

局部提升性质（LLP）是$\mathrm｛C｝^*$-代数之间完全正映射的投影性的局部版本。在核情况之外，很少有$\mathrm{C}^*$-代数已知具有LLP\@。本文证明了由Hadwin引入并由Loring和Shulman进一步研究的代数收缩$\mathrm{C}^*$-代数的LLP成立。我们还证明了Brothier和Jones引入的泛勾股$\mathrm{C}^*$-代数具有提升性质。

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Universal $C^∗$-algebras with the local lifting property

The Local Lifting Property (LLP) is a localized version of projectivity for completely positive maps between $\mathrm{C}^*$-algebras. Outside of the nuclear case, very few $\mathrm{C}^*$-algebras are known to have the LLP\@. In this article, we show that the LLP holds for the algebraic contraction $\mathrm{C}^*$-algebras introduced by Hadwin and further studied by Loring and Shulman. We also show that the universal Pythagorean $\mathrm{C}^*$-algebras introduced by Brothier and Jones have the Lifting Property.

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