Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2017
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1711.09771 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917556979236864 |
|---|---|
| author | Beil, Charlie |
| author_facet | Beil, Charlie |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_09771 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Dimer algebras, ghor algebras, and cyclic contractions Beil, Charlie Rings and Algebras High Energy Physics - Theory Representation Theory 16G20, 16S38, 16S50 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. |
| title | Dimer algebras, ghor algebras, and cyclic contractions |
| topic | Rings and Algebras High Energy Physics - Theory Representation Theory 16G20, 16S38, 16S50 |
| url | https://arxiv.org/abs/1711.09771 |