Mathematics – Representation Theory
Scientific paper
2008-10-29
Mathematics
Representation Theory
16 pages
Scientific paper
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 summands of $T$. In this paper, we prove that a partial tilting $A^{(m)}$-module $T$ is a tilting $A^{(m)}$-module if and only if $\delta (T)=\delta (A^{(m)})$, and that every partial tilting $A^{(m)}$-module has complements. As an application, we deduce that the tilting quiver $\mathscr{K}_{A^{(m)}}$ of $A^{(m)}$ is connected. Moreover, we investigate the number of complements to almost tilting modules over duplicated algebras.
No associations
LandOfFree
Partial tilting modules over $m$-replicated algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Partial tilting modules over $m$-replicated algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Partial tilting modules over $m$-replicated algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-71686