1. REDUCTION OF CLUSTER ITERATION MAPS.
- Author
-
CRUZ, INÊS and SOUSA-DIAS, M. ESMERALDA
- Subjects
- *
ITERATIVE methods (Mathematics) , *DIFFERENCE equations , *CLUSTER algebras , *SUBMANIFOLDS , *GEOMETRY - Abstract
We study iteration maps of difference equations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and presymplectic geometry, we show that these cluster iteration maps can be reduced to symplectic maps on a lower dimensional submanifold, provided the matrix representing the quiver is singular. The reduced iteration map is explicitly computed for several periodic quivers using either the presymplectic reduction or a Poisson reduction via log-canonical Poisson structures. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF