2014/07/28 by Zhang Yingbo, Yingbo, Zhang, Xu Yunge +1
Mathematics · #15A21 #16G20 #16G60 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:15A21 #msc:16G20 #msc:16G60
paper · pdf · doi:10.48550/arxiv.1407.7576
72 pages,22 figures. arXiv admin note: substantial text overlap with arXiv:1403.5930
arxiv created 2014/07/28 · arxiv updated 2014/07/30
The celebrated Drozd's theorem asserts that a finite-dimensional basic algebra Λ over an algebraically closed field k is either tame or wild, whereas the Crawley-Boevey's theorem states that given a tame algebra Λ and a dimension d, all but finitely many 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 inverse of Crawley-Boevey's theorem, which gives an internal description of tameness in terms of Auslander-Reiten quivers.