{"paper":{"title":"Re-gauging groupoid, symmetries and degeneracies for Graph Hamiltonians and applications to the Gyroid wire network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Birgit Wehefritz-Kaufmann, Ralph M. Kaufmann, Sergei Khlebnikov","submitted_at":"2012-08-16T02:32:07Z","abstract_excerpt":"We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)--commutative geometries. By selecting gauging data these geometries are realized by matrices through an explicit construction or a Kan-extension. We describe the changes in gauge via the action of a regauging groupoid. It acts via matrices that give rise to a noncommutative 2--cocycle and hence to a groupoid extension (gerbe).\n  We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of regaugings. In the commutative case"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3266","kind":"arxiv","version":2},"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"}