Leszczyński, Zbigniew; Skowroński, Andrzej Tame triangular matrix algebras. (English) Zbl 0978.16014 Colloq. Math. 86, No. 2, 259-303 (2000). Let \(A\) be a finite dimensional \(k\)-algebra for \(k\) algebraically closed, such that the triangular matrix algebra \(T_2(A)\) is tame. It is known that in this case, \(A\) is of finite representation type and standard. In this paper, the authors describe, in terms of full, convex subcategories of \(\widetilde A\) (the universal Galois covering of \(A\)) all algebras \(A\) such that \(T_2(A)\) is tame. Moreover, there is also a complete classification of these algebras in finite representation type, domestic type, of polynomial growth, and tame type.As a consequence there is also a classification for the Auslander algebras \({\mathbf A}(A)\). For this purpose, they list the families \(\mathbf W\), \(\mathbf{NPG}\), \(\mathbf{ND}\) and \(\mathbf{IT}\). So, \(T_2(A)\) is tame if and only if \(\widetilde A\) does not contain a finite full convex subcategory of the \(\mathbf W\) family and in a similar way, for the other families. The proof is done by a case by case inspection of all possible finite full convex subcategories of \(T_2(A)\). Reviewer: Gladys Chalom (São Paulo) Cited in 7 Documents MSC: 16G60 Representation type (finite, tame, wild, etc.) of associative algebras 16S50 Endomorphism rings; matrix rings 16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 16G30 Representations of orders, lattices, algebras over commutative rings Keywords:finite representation type; classification by convex subcategories; Galois coverings; triangular matrix algebras; tame representation type; domestic type; algebras of polynomial growth; Auslander algebras PDFBibTeX XMLCite \textit{Z. Leszczyński} and \textit{A. Skowroński}, Colloq. Math. 86, No. 2, 259--303 (2000; Zbl 0978.16014) Full Text: DOI EuDML