The structure of group \(C^*\)-algebras of the generalized Dixmier groups (Q1425470)
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scientific article; zbMATH DE number 2061196
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The structure of group \(C^*\)-algebras of the generalized Dixmier groups |
scientific article; zbMATH DE number 2061196 |
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The structure of group \(C^*\)-algebras of the generalized Dixmier groups (English)
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21 March 2004
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Summary: In this paper, we first analyze the algebraic structure of group \(C^*\)-algebras of the generalized Dixmier groups, and next consider that of group \(C^*\)-algebras of some Lie semi-direct products with multi-diagonal or diagonal actions. As an application, we estimate the stable rank and the connected stable rank of these \(C^*\)-algebras in terms of groups. Also, we show that some of these group \(C^*\)-algebras have no nontrivial projections.
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group \(C^*\)-algebras
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stable rank
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