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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1711.09771 |
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Table of Contents:
- A ghor algebra is the path algebra of a dimer quiver on a surface, modulo relations that come from the perfect matchings of its quiver. Such algebras arise from abelian quiver gauge theories in physics. We show that a ghor algebra $Λ$ on a torus is a dimer algebra (a quiver with potential) if and only if it is noetherian, and otherwise $Λ$ is the quotient of a dimer algebra by homotopy relations. Furthermore, we classify the simple $Λ$-modules of maximal dimension and give an explicit description of the center of $Λ$ using a special subset of perfect matchings. In our proofs we introduce formalized notions of Higgsing and the mesonic chiral ring from quiver gauge theory.