Type $G_2$ Quantum Subgroups from Graph Planar Algebra Embeddings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917191396360192 |
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| author | Hill, Caleb Kennedy |
| author_facet | Hill, Caleb Kennedy |
| contents | We give graphical presentations for the two quantum subgroups of type $G_2$. To do this we use a method of extending a tensor category by embedding the planar algebra of a $\otimes$-generating object into the graph planar algebra of this object's fundamental graph. This allows the use of computational methods to uncover relations we would have little hope of arriving at otherwise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Type $G_2$ Quantum Subgroups from Graph Planar Algebra Embeddings Hill, Caleb Kennedy Quantum Algebra Mathematical Physics Representation Theory We give graphical presentations for the two quantum subgroups of type $G_2$. To do this we use a method of extending a tensor category by embedding the planar algebra of a $\otimes$-generating object into the graph planar algebra of this object's fundamental graph. This allows the use of computational methods to uncover relations we would have little hope of arriving at otherwise. |
| title | Type $G_2$ Quantum Subgroups from Graph Planar Algebra Embeddings |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2601.05381 |