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Annular SL(2) and SL(3) web algebras
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Annular SL(2) and SL(3) web algebras
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Paper
Annular SL(2) and SL(3) web algebras
2025
Overview
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.
Publisher
Cornell University Library, arXiv.org
Subject
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