{"paper":{"title":"Smash products of group weighted bound quivers and Brauer graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hideto Asashiba","submitted_at":"2017-09-27T00:10:41Z","abstract_excerpt":"Let $\\Bbbk$ be a field, $G$ a group, and $(Q, I)$ a bound quiver. A map $W\\colon Q_1 \\to G$ is called a $G$-weight on $Q$, which defines a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$, and $W$ is called homogeneous if $I$ is a homogeneous ideal of the $G$-graded $\\Bbbk$-category $\\Bbbk(Q, W)$. Then we have a $G$-graded $\\Bbbk$-category $\\Bbbk(Q, I, W):= \\Bbbk(Q, W)/I$. We can then form a smash product $\\Bbbk(Q, I, W)\\# G$ of $\\Bbbk(Q, I, W)$ and $G$, which canonically defines a Galois covering $\\Bbbk(Q, I, W)\\# G \\to \\Bbbk(Q, I)$ with group $G$ (we will see that all such Galois coverings to $\\Bbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09289","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"}