{"paper":{"title":"Tensor Products of Classifiable C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Huaxin Lin, Wei Sun","submitted_at":"2012-03-16T15:29:10Z","abstract_excerpt":"Let ${\\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\\cal Z}$-stable $C^*$-algebras in ${\\cal A}_1$ which satisfy the Universal Coefficient Theorem can be classified up to isomorphism by the Elliott invariant. We show that $A\\in {\\cal A}_1$ if and only if $A\\otimes B$ has tracial rank at most one for one of unital simple infinite dimensional AF-algebra $B.$ In fact, we show that $A\\in {\\cal A}_1$ if and only if $A\\otimes B\\in {\\cal A}_1$ for so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3737","kind":"arxiv","version":3},"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"}