Annular SL(2) and SL(3) web algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913979280916480 |
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| author | Akhmechet, Rostislav Khovanov, Mikhail Zhang, Melissa |
| author_facet | Akhmechet, Rostislav Khovanov, Mikhail Zhang, Melissa |
| contents | We use annular foam TQFTs introduced by the first two authors to define equivariant $SL(2)$ and $SL(3)$ web algebras in the annulus. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras whose chain homotopy type is an invariant of the tangle. Several properties of algebras and bimodules are established. An essential technical part of the paper provides a bijective correspondence between non-elliptic annular $SL(3)$ webs and closed paths in the $SL(3)$ weight lattice. This generalizes an analogous bijection in the planar setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Annular SL(2) and SL(3) web algebras Akhmechet, Rostislav Khovanov, Mikhail Zhang, Melissa Geometric Topology Quantum Algebra 57K18, 57K16, 18N25 We use annular foam TQFTs introduced by the first two authors to define equivariant $SL(2)$ and $SL(3)$ web algebras in the annulus. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras whose chain homotopy type is an invariant of the tangle. Several properties of algebras and bimodules are established. An essential technical part of the paper provides a bijective correspondence between non-elliptic annular $SL(3)$ webs and closed paths in the $SL(3)$ weight lattice. This generalizes an analogous bijection in the planar setting. |
| title | Annular SL(2) and SL(3) web algebras |
| topic | Geometric Topology Quantum Algebra 57K18, 57K16, 18N25 |
| url | https://arxiv.org/abs/2508.05605 |