Quasidiagonality of $C^{\ast }$-algebras of solvable Lie groups

Abstract

We characterize the solvable Lie groups of the form ${\mathbb{R}}^m⋊\mathbb{R}$, whose $C^{\ast }$-algebras are quasidiagonal. Using this result, we determine the connected simply connected solvable Lie groups of type~I whose $C^{\ast }$-algebras are strongly quasidiagonal. As a by-product, we give also examples of amenable Lie groups with non-quasidiagonal $C^{\ast }$-algebras.

arXiv comment19 pages, Integral Equations and Operator Theory

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