{"paper":{"title":"$C^*$ exponential length of commutators unitaries in $AH$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Chun Guang Li, Iv\\'an Vel\\'azquez Ruiz, Liangqing Li","submitted_at":"2018-07-24T10:26:53Z","abstract_excerpt":"For each unital $C^*$-algebra $A$, we denote $cel_{CU}(A)=\\sup\\{cel(u):u\\in CU(A)\\}$, where $cel(u)$ is the exponential length of $u$ and $CU(A)$ is the closure of the commutator subgroup of $U_0(A)$. In this paper, we prove that $cel_{CU}(A)=2\\pi$ provided that $A$ is an $AH$ algebras with slow dimension growth whose real rank is not zero. On the other hand, we prove that $cel_{CU}(A)\\leq 2\\pi$ when $A$ is an $AH$ algebra with ideal property and of no dimension growth (if we further assume $A$ is not of real rank zero, we have $cel_{CU}(A)= 2\\pi$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09018","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}