Group splittings and integrality of traces (Q1001227)
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scientific article; zbMATH DE number 5508258
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Group splittings and integrality of traces |
scientific article; zbMATH DE number 5508258 |
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Group splittings and integrality of traces (English)
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16 February 2009
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The integrality of the trace conjecture for torsion-free groups \(G\) is the assertion that the trace of any idempotent matrix over the reduced \(C^*\)-algebra \(\mathbb C*G\) is an integer. Connes proved the conjecture for free groups using their actions on trees. The author elaborates on Connes' proof and shows that the trace is integer for some idempotent matrices when \(G\) acts on a tree.
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traces
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Baum-Connes conjecture
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\(K_0\)-group
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group actions on trees
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