Quiver mutations

quiver

• quiver = finite oriented graph without loop and 2-cycle

 

quiver mutations

• This is a process that can be done at any point of the quiver
• The new quiver has same points as the old quiver.
• Arrows into the point of mutation in the old quiver becomes arrows out, in the new quiver.
• Arrows out of the point of mutation in the old quiver becomes arrows into, in the new quiver.
• There are new arrows formed. Any path of length 2 through the point of mutation gives an arrow in the new quiver. The arrow has the same startining and ending points as the path.
• The new arrows simplify with any old arrows in the opposite direction.

 

links

• http://www.mutatingquivers.com/Home.html
• http://www.mutatingquivers.com/Concept%20of%20Mutation.html
• http://mathoverflow.net/questions/36536/quiver-mutation

related items

• Exchange relations of cluster algebras
• quiver representations