Quasidiagonality of C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-Algebras of Solvable Lie Groups

被引：0
作者：
Ingrid Beltiţă
Daniel Beltiţă
机构：
[1] Institute of Mathematics “Simion Stoilow” of the Romanian Academy,
来源：
Integral Equations and Operator Theory | 2018年 / 90卷 / 1期
关键词：
Unitary dual; -Group; Solvable Lie group; Quasidiagonal ; -algebra; Primary 22D25; Secondary 22E27;
D O I：
10.1007/s00020-018-2438-6
中图分类号：
学科分类号：
摘要：
We characterize the solvable Lie groups of the form Rm⋊R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^m\rtimes {\mathbb {R}}$$\end{document}, whose C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebras are quasidiagonal. Using this result, we determine the connected simply connected solvable Lie groups of type I whose C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebras are strongly quasidiagonal. As a by-product, we give also examples of amenable Lie groups with non-quasidiagonal C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^*$$\end{document}-algebras.
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