Concept of mutation of quivers
The term 'mutation' comes from biological sciences and refers to the process by which organisms (especially viruses) are transformed into other forms. For examlpe, strains of HIV, Tuberculosis, Flu viruses can mutate to different strains which are more resistant to medication.
The term has a similar meaning in mathematics. Mutation of quivers is an operation that treansforms a quiver into another quiver of the same family. Unlike in biological sciences where mutation may not be reversible, the process of mutation of quivers is reversible.
This operation is very simple to perform, and with the aid of the mutation applet, it becomes more imteresting.
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.