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In particular, if $C_{\\lambda}^*(T)$ is simple then $F$ is not amenable. Here we prove the converse, namely, if $F$ is not amenable then we can find two sets $H_1"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1409.8099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"d62850068cffdca549b578d53dbedf816689dcd67eadadc189256409f3cf9f11","abstract_canon_sha256":"8ce6fae064008451c57f560fb4d57e2ce01d8fdbeeaa74df2a2dde8d57502d11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:03.179574Z","signature_b64":"AiazodZSdcSWvloQkF0lB4aCIeNKf0Gs0AbiZpyo0s8Z9tf889BaNWeqGDSEcXszeTlBw3ZTWqycBO/87cTSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","last_reissued_at":"2026-05-18T02:41:03.179063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:03.179063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideal structure of the C*-algebra of Thompson group T","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Collin Bleak, Kate Juschenko","submitted_at":"2014-09-29T12:45:10Z","abstract_excerpt":"In a recent paper Uffe Haagerup and Kristian Knudsen Olesen show that for Richard Thompson's group $T$, if there exists a finite set $H$ which can be decomposed as disjoint union of sets $H_1$ and $H_2$ with $\\sum_{g\\in H_1}\\pi(g)=\\sum_{h\\in H_2}\\pi(h)$ and such that the closed ideal generated by $\\sum_{g\\in H_1}\\lambda(g)-\\sum_{h\\in H_2}\\lambda(h)$ coincides with $C^*_\\lambda(T)$, then the Richard Thompson group $F$ is not amenable. In particular, if $C_{\\lambda}^*(T)$ is simple then $F$ is not amenable. 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