{"paper":{"title":"Stability of the centers of group algebras of general affine groups $GA_n(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jinkui Wan, Lan Zhou","submitted_at":"2025-06-06T00:49:10Z","abstract_excerpt":"The general affine group $GA_n(q)$ consisting of invertible affine transformations of an affine space of codimension one in the vector space $\\mathbb{F}_q^n$ over a finite field $\\mathbb{F}_q$, can be viewed as a subgroup of the general linear group $GL_{n}(q)$ over $\\mathbb{F}_q$. In the article, we introduce the notion of the type of each matrix in $GA_n(q)$ and give an explicit representative for each conjugacy class. Then the center $\\mathscr{A}_n(q)$ of the integral group algebra $\\mathbb{Z}[GA_n(q)]$ is proved to be a filtered algebra via the length function defined via the reflections l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05652","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05652/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}