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

IF 0.3 4区数学 Q4 MATHEMATICS

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

Kristin Courtney

引用次数: 7

Abstract

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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具有局部提升性质的泛$C^ * $代数

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.