Tilting mutation for $m$-replicated algebras

Hongbo Lv; Shunhua Zhang

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arXiv · 0903.0958

Tilting mutation for $m$-replicated algebras

Hongbo Lv·Shunhua Zhang

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Abstract

Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $A^{(m)}$ be the $m$-replicated algebra of $A$ and $\mathscr{C}_{m}(A)$ be the $m$-cluster category of $ A$. We investigate properties of complements to a faithful almost complete tilting $A^{(m)}$-module and prove that the $m$-cluster mutation in $\mathscr{C}_{m}(A)$ can be realized in ${\rm mod} A^{(m)}$, which generalizes corresponding results on duplicated algebras established in [Z1].

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Hongbo Lv, Shunhua Zhang. 2009-03-05. Tilting mutation for $m$-replicated algebras. https://arxiv.org/abs/0903.0958

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