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AR-components for generalized Beilinson algebras


Author: Julia Worch
Journal: Proc. Amer. Math. Soc. 143 (2015), 4271-4281
MSC (2010): Primary 16G20, 16G70; Secondary 16S90, 16S37
DOI: https://doi.org/10.1090/S0002-9939-2015-12621-4
Published electronically: March 31, 2015
MathSciNet review: 3373926
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Abstract: We show that the generalized $ W$-modules defined in 2013 determine $ \mathbb{Z}A_{\infty }$-components in the Auslander-Reiten quiver $ \Gamma (n,r)$ of the generalized Beilinson algebra $ B(n,r)$, $ n \geq 3$. These components entirely consist of modules with the constant Jordan type property. We arrive at this result by interpreting $ B(n,r)$ as an iterated one-point extension of the $ r$-Kronecker algebra $ \mathcal {K}_r$, which enables us to generalize findings concerning the Auslander-Reiten quiver $ \Gamma (\mathcal {K}_r)$ presented in 2013 to $ \Gamma (n,r)$.


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Additional Information

Julia Worch
Affiliation: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
Email: jworch@gmx.net

DOI: https://doi.org/10.1090/S0002-9939-2015-12621-4
Received by editor(s): January 23, 2014
Received by editor(s) in revised form: June 22, 2014
Published electronically: March 31, 2015
Additional Notes: The author’s research was partly supported by the D.F.G. priority program SPP 1388 “Darstellungstheorie”
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2015 American Mathematical Society

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