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Forbidden Subcategories of Non-Polynomial Growth Tame Simply Connected Algebras

Published online by Cambridge University Press:  20 November 2018

J. A. De La Peña  and
A. Skowroński
J. A. De La Peña
Affiliation:
Instituto de Matemáticas, UNAM Ciudad Universitaria México 04510 D.F. México
A. Skowroński
Affiliation:
Faculty of Mathematics and Informatics Nicholas Copernicus University Chopina 12/18 87-100 Toruń Poland
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Abstract

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Let k be an algebraically closed field and A = kQ/I be a basic finite dimensional k-algebra such that Q is a connected quiver without oriented cycles. Assume that A is strongly simply connected, that is, for every convex subcategory B of A the first Hochschild cohomology H1(B, B) vanishes. The algebra A is sincere if it admits an indecomposable module having all simples as composition factors. We study the structure of strongly simply connected sincere algebras of tame representation type. We show that a sincere, tame, strongly connected algebra A which contains a convex subcategory which is either representation-infinite tilted of type Ẽp, p = 6,7,8, or a tubular algebra, is of polynomial growth.

Keywords

16G1016G60
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 5 , 01 October 1996 , pp. 1018 - 1043
Copyright
Copyright © Canadian Mathematical Society 1996

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