Tilting mutation for $m$-replicated algebras

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 ${\mathcal{C}}_m(A)$ 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 ${\mathcal{C}}_m(A)$ can be realized in $\mathrm{mod}{A}^{(m)}$, which generalizes corresponding results on duplicated algebras established in [Z1].

17 pages

References in corpus (3)

• On triangulated orbit categories
• Tilting theory and cluster algebras
• Cluster combinatorics of d-cluster categories

Cited by in corpus (1)

• Endomorphism algebras arising from mutations