AR-components for generalized Beilinson algebras

Worch, Julia

doi:10.1090/S0002-9939-2015-12621-4

AR-components for generalized Beilinson algebras
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Proc. Amer. Math. Soc. 143 (2015), 4271-4281 Request permission

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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