{"paper":{"title":"Representation dimensions of triangular matrix algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hongbo Yin, Shunhua Zhang","submitted_at":"2011-07-19T23:59:03Z","abstract_excerpt":"Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $T_2(A)=(\\begin{array}{cc}A&0 A&A\\end{array})$ be the triangular matrix algebra and $A^{(1)}=(\\begin{array}{cc}A&0 DA&A\\end{array})$ be the duplicated algebra of $A$ respectively. We prove that ${\\rm rep.dim}\\ T_2(A)$ is at most three if $A$ is Dynkin type and ${\\rm rep.dim}\\ T_2(A)$ is at most four if $A$ is not Dynkin type. Let $T$ be a tilting A-$\\module$ and $\\ol{T}=T\\oplus\\ol{P}$ be a tilting $A^{(1)}$-$\\module$. We show that $\\End_{A^{(1)}} \\ol{T}$ is representation finite if and only if the full s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3865","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"}