{"paper":{"title":"The quantum adjacency algebra and subconstituent algebra of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Paul Terwilliger","submitted_at":"2017-10-16T22:12:01Z","abstract_excerpt":"Let $\\Gamma$ denote a finite, undirected, connected graph, with vertex set $X$. Fix a vertex $x \\in X$. Associated with $x$ is a certain subalgebra $T=T(x)$ of ${\\rm Mat}_X(\\mathbb C)$, called the subconstituent algebra. The algebra $T$ is semisimple. Hora and Obata introduced a certain subalgebra $Q \\subseteq T$, called the quantum adjacency algebra. The algebra $Q$ is semisimple. In this paper we investigate how $Q$ and $T$ are related. In many cases $Q=T$, but this is not true in general. To clarify this issue, we introduce the notion of quasi-isomorphic irreducible $T$-modules. We show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06011","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"}