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<p>We define equivariant annular <i>SL</i>(2) and <i>SL</i>(3) web algebras using annular foam TQFTs introduced by the first two authors. To a tangle in the thickened annulus we associate a complex of bimodules over these algebras and prove its invariance up to chain homotopy under annular isotopy. Our constructions extend the known planar story to the equivariant annular setting, where winding phenomena and additional gradings enter naturally. An essential technical part of the paper provides a bijective correspondence between non-elliptic annular <i>SL</i>(3) webs and closed paths in the <i>SL</i>(3) weight lattice. This generalizes an analogous bijection in the planar setting and implies that the algebras have finite rank over the ground ring.</p>

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Annular SL(2) and SL(3) web algebras

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Rostislav Akhmechet,
  • Mikhail Khovanov,
  • Melissa Zhang

摘要

We define equivariant annular SL(2) and SL(3) web algebras using annular foam TQFTs introduced by the first two authors. To a tangle in the thickened annulus we associate a complex of bimodules over these algebras and prove its invariance up to chain homotopy under annular isotopy. Our constructions extend the known planar story to the equivariant annular setting, where winding phenomena and additional gradings enter naturally. 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 and implies that the algebras have finite rank over the ground ring.