$C^*$-rigidity for certain exponential Lie groups

Abstract: A exponential Lie group is called (stably) $C^*$-rigid if it is uniquely determined, within the class of exponential Lie groups, by the class of isomorphism (Morita equivalence) of its $C^*$ algebra. We discuss the problem of $C^*$-rigidity of exponential Lie groups. In particular, we show that generalized $ax+b$-groups are non-rigid, while nilpotent Lie groups of dimension less than equal to 5 are stably $C^*$-rigid.

functional analysisoperator algebras

Audience: advanced learners

Functional analysis and operator algebras in Athens

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