Cluster-tilted algebras as trivial extensions

Details Cluster-tilted algebras as trivial extensions Cluster-tilted algebras as trivial extensions

2006-01-23

arxiv.org/abs/math/0601537v1

Mathematics

Representation Theory

14 pages

Scientific paper

Given a finite dimensional algebra $C$ (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension $C\ltimes \Ext_C^2(DC,C)$ of $C$ by the $C$-$C$-bimodule $\Ext_C^2(DC,C)$. We give a construction for the quiver of the relation-extension algebra in case the quiver of $C$ has no oriented cycles. Our main result says that an algebra $\tilde C$ is cluster-tilted if and only if there exists a tilted algebra $C$ such that $\tilde C$ is isomorphic to the relation-extension of $C$.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-601546