Prime ideals in the \(C^*\)-algebra of a nilpotent group (Q1070048)
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scientific article; zbMATH DE number 3933356
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Prime ideals in the \(C^*\)-algebra of a nilpotent group |
scientific article; zbMATH DE number 3933356 |
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Prime ideals in the \(C^*\)-algebra of a nilpotent group (English)
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1986
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In this note we show that for a locally compact nilpotent group G, having a compactly generated open normal subgroup, closed prime ideals in \(C^*(G)\) are always maximal ones. This implies that Prim(G) is then a \(T_ 1\)-topological space. The proofs depend heavily on the structure theorems for compactly generated nilpotent locally compact groups.
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\(C^*\)-algebra
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nilpotent group
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prime ideals
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locally compact groups
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