Toric CY-3 algebras and quiver polyhedra
Raf Bocklandt (University of Antwerp)
Wednesday 28th January, 2009 15:00-16:00 Mathematics Building, room 326
Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi Yau Algebras. These algebras share some specific properties: they are (1) positively graded, (2) the relations are all of the form p-q where p and q are paths in a connected quiver and (3) the algebras are prime and finitely generated modules over their centers. We show that all 3-dimensional Calabi Yau algebras that satisfy the first two conditions can be constructed from a quiver polyhedron, which is a generalization of a dimer model. If the algebra also satisfies the third condition the algebra comes from a dimer model.