Calabi Yau algebras and weighted quiver polyhedra
Abstract
Dimer models have been used in string theory to construct path algebras with relations that are 3-dimensional Calabi-Yau Algebras. These constructions result in algebras that share some specific properties: they are finitely generated modules over their centers and their representation spaces are toric varieties. In order to describe these algebras we introduce the notion of a toric order and show that all toric orders which are 3-dimensional Calabi-Yau algebras can be constructed from dimer models on a torus. Toric orders are examples of a much broader class of algebras: positively graded cancellation algebras. For these algebras the CY-3 condition implies the existence of a weighted quiver polyhedron, which is an extension of dimer models obtained by replacing the torus with any two-dimensional compact orientable orbifold.
Keywords
Cite
@article{arxiv.0905.0232,
title = {Calabi Yau algebras and weighted quiver polyhedra},
author = {Raf Bocklandt},
journal= {arXiv preprint arXiv:0905.0232},
year = {2011}
}
Comments
Original paper was expanded and split in 2. The is the first part which discusses quiver polyhedra and how they arise from CY3-algebras. The second part discusses consistency conditions and is called 'Consistency conditions for dimer models'