{"paper":{"title":"On Conjugacy of MASAs in Graph $C^*$-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jeong Hee Hong, Tomohiro Hayashi, Wojciech Szymanski","submitted_at":"2016-04-25T01:50:19Z","abstract_excerpt":"For a large class of finite graphs $E$, we show that whenever $\\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph $C^*$-algebra $C^*(E)$ such that $\\alpha({\\mathcal D}_E) \\neq{\\mathcal D}_E$, where ${\\mathcal D}_E$ is the canonical MASA in $C^*(E)$, then $\\alpha({\\mathcal D}_E)\\neq w{\\mathcal D}_E w^*$ for all unitaries $w\\in C^*(E)$. That is, the two MASAs ${\\mathcal D}_E$ and $\\alpha({\\mathcal D}_E)$ of $C^*(E)$ are outer but not inner conjugate. Passing to an isomorphic $C^*$-algebra by changing the underlying graph makes this result applicable to certain non quas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07105","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"}