Quiver mutations

• http://www.mutatingquivers.com/Home.html
• http://mathoverflow.net/questions/36536/quiver-mutation
• quiver representations

 

 

quiver

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

 

 

quiver mutations

Process of mutation
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.

 

http://www.mutatingquivers.com/Concept%20of%20Mutation.html