# Partial tilting modules over $m$-replicated algebras - Mathematics > Representation Theory

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Abstract: Let $A$ be a hereditary algebra over an algebraically closed field $k$ and$A^{m}$ be the $m$-replicated algebra of $A$. Given an $A^{m}$-module $T$,we denote by $\delta T$ the number of non isomorphic indecomposable summandsof $T$. In this paper, we prove that a partial tilting $A^{m}$-module $T$ isa tilting $A^{m}$-module if and only if $\delta T=\delta A^{m}$, andthat every partial tilting $A^{m}$-module has complements. As an application,we deduce that the tilting quiver $\mathscr{K} {A^{m}}$ of $A^{m}$ isconnected. Moreover, we investigate the number of complements to almost tiltingmodules over duplicated algebras.

Author: Shunhua Zhang

Source: https://arxiv.org/