Mutation of cluster-tilting objects and potentials

arxiv: 0804.3813 · v4 · pith:GEF32FSJnew · submitted 2008-04-23 · 🧮 math.RT · math.RA

Mutation of cluster-tilting objects and potentials

Aslak Bakke Buan , Osamu Iyama , Idun Reiten , David Smith This is my paper

classification 🧮 math.RT math.RA

keywords algebrasjacobianmutationpotentialsquiverscluster-tiltingcy-tiltedmodules

0 comments p. Extension

pith:GEF32FSJ Add to your LaTeX paper

What is a Pith Number?

\usepackage{pith}
\pithnumber{GEF32FSJ}

Prints a linked pith:GEF32FSJ badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more

read the original abstract

We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This gives a close connection between 2-CY-tilted algebras and Jacobian algebras associated with quivers with potentials. We show that cluster-tilted algebras are Jacobian and also that they are determined by their quivers. There are similar results when dealing with tilting modules over 3-CY algebras. The nearly Morita equivalence for 2-CY-tilted algebras is shown to hold for the finite length modules over Jacobian algebras.

This paper has not been read by Pith yet.

Mutation of cluster-tilting objects and potentials

discussion (0)