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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Gradings of $ {\bf B}\sb{n}$ and $ {\bf C}\sb{n}$ of finite representation type


Authors: Ibrahim Assem and Oscar Roldán
Journal: Trans. Amer. Math. Soc. 279 (1983), 589-609
MSC: Primary 16A48; Secondary 16A46, 16A64
DOI: https://doi.org/10.1090/S0002-9947-1983-0709570-1
MathSciNet review: 709570
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Abstract: It was shown by Bongartz and Gabriel that the classification of simplyconnected algebras (i.e. finite-dimensional, basic, of finite representation type and with a simply-connected Auslander-Reiten graph) can be reduced to the study of certain numerical functions, called gradings, operating on a tree. Here, we classify in terms of their bounden species the simply-connected algebras arising from gradings of the Dynkin trees $ {{\mathbf{B}}_n}$ and $ {{\mathbf{C}}_n}$, and show that these are exactly the tilted algebras of types $ {{\mathbf{B}}_n}$ and $ {{\mathbf{C}}_n}$, respectively.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0709570-1
Keywords: Gradings, simply-connected algebras, tilted algebras, bounden species
Article copyright: © Copyright 1983 American Mathematical Society