## Gradings of $\textbf {B}_{n}$ and $\textbf {C}_{n}$ of finite representation type

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- by Ibrahim Assem and Oscar Roldán
- Trans. Amer. Math. Soc.
**279**(1983), 589-609 - DOI: https://doi.org/10.1090/S0002-9947-1983-0709570-1
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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.## References

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## Bibliographic Information

- © Copyright 1983 American Mathematical Society
- 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