| dc.description.abstract | In recent times, there has been a lot of interest in the study of quivers,
both by mathematicians and theoretical physicists. We introduce a new
concept of polar quivers and their mutation. The idea of polar quivers
arises from the concept of anomaly free R-charges in theoretical physics.
Mutation of polar quivers is build on mutation quivers with potential,
which was defined by Derksen, Weyman and Zelevinsky. An R-charge assigns
angles to the arrows of a quiver. In a polar quiver we assign angles
and positive non-zero integers to vertices and impose conditions equivalent
to the anomaly conditions for R-charges. We then establish that
mutation of a polar quiver will give a polar quiver if and only if a simple
additional condition is satisfied. We use families of quivers linked by mutation,
from the work of Stern, as our source of examples. The results of
this study have applications in geometry and theoretical physics. | en_US |
