2014/03/24 by Yingbo Zhang, Zhang, Yingbo, Yunge Xu +1 · 1 citation
Mathematics · Physics and Astronomy · #15A21 #16G20 #16G60 #16G70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:15A21 #msc:16G20 #msc:16G60 #msc:16G70
paper · pdf · doi:10.48550/arxiv.1403.5930
62 pages, 12 figures
arxiv created 2014/03/24 · openalex publication_date 2014/03/24 · arxiv updated 2014/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Λ be a finite-dimensional basic algebra over an algebraically closed field k. The well-known Drozd's theorem asserts, that Λ is either tame or wild. The Crawley-Boevey's Theorem states that for a given tame algebra Λ, and for each dimension d almost all isomorphism classes of indecomposable Λ-modules of dimension d are isomorphic to their Auslander-Reiten translations and hence belong to homogeneous tubes. In this paper we prove the converse of Crawley-Boevey's Theorem and thus give an internal description of tameness in terms of AR-quivers. This gives a complete answer to a question posed by Ringel in \citeR1.