{"paper":{"title":"On the representation dimension of smash products","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chonghui Huang, Lijing Zheng, Qianhong Wan","submitted_at":"2016-03-03T02:57:05Z","abstract_excerpt":"Let $A$ be a finite dimensional $G$-graded algebra with $G$ a finite group, and $A\\# k[G]^{\\ast}$ be the smash product of $A$ with the group $G$. Our results can be stated as follows: (1) If $A$ is a self-injective algebra and separably graded, then the dimensions of triangulated categories $\\underline{\\rm mod}A$ and $\\underline{\\rm mod}A\\# k[G]^{\\ast}$ are equal. In particular, we obtain that the representation dimension of $A\\# k[G]^{\\ast}$ is at least the dimension of triangulated category $\\underline{\\rm mod}A$ plus 2; (2) Generally, if $A$ is a $k$-algebra and separably graded, then the O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00953","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"}