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arXiv · 1711.09771

Dimer algebras, ghor algebras, and cyclic contractions

Charlie Beil
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Abstract

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 $\Lambda$ on a torus is a dimer algebra (a quiver with potential) if and only if it is noetherian, and otherwise $\Lambda$ is the quotient of a dimer algebra by homotopy relations. Furthermore, we classify the simple $\Lambda$-modules of maximal dimension and give an explicit description of the center of $\Lambda$ 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.

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Charlie Beil. 2017-11-27. Dimer algebras, ghor algebras, and cyclic contractions. https://doi.org/10.1007/s10468-023-10224-y

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