Cluster-tilted algebras of type $D_n$

Details Cluster-tilted algebras of type $D_n$ Cluster-tilted algebras of type $D_n$

2008-12-03

arxiv.org/abs/0812.0650v3

Mathematics

Representation Theory

21 pages, 13 figures, accepted for publication in Comm.Algebra

Scientific paper

Let $H$ be a hereditary algebra of Dynkin type $D_n$ over a field $k$ and $\mathscr{C}_H$ be the cluster category of $H$. Assume that $n\geq 5$ and that $T$ and $T'$ are tilting objects in $\mathscr{C}_H$. We prove that the cluster-tilted algebra $\Gamma=\mathrm{End}_{\mathscr{C}_H}(T)^{\rm op}$ is isomorphic to $\Gamma'=\mathrm{End}_{\mathscr{C}_H}(T')^{\rm op}$ if and only if $T=\tau^iT'$ or $T=\sigma\tau^jT'$ for some integers $i$ and $j$, where $\tau$ is the Auslander-Reiten translation and $\sigma$ is the automorphism of $\mathscr{C}_H$ defined in section 4.

Affiliated with

Also associated with

No associations

Rating

Cluster-tilted algebras of type $D_n$ 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 Cluster-tilted algebras of type $D_n$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cluster-tilted algebras of type $D_n$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-624863