Odd annular Bar-Natan category and gl(1 | 1)

Casey Necheles, Stephan Wehrli

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we introduce two monoidal supercategories: the odd dotted Temperley-Lieb category TLo,•(σ), which is a generalization of the odd Temperley-Lieb category studied by Brundan and Ellis in [Monoidal Supercategories, Commun. Math. Phys. 351 (2017) 1045-1089], and the odd annular Bar-Natan category BNo(A), which generalizes the odd Bar-Natan category studied by Putyra in [A 2-category of chronological cobordisms and odd Khovanov homology, Banach Center Publ. 103 (2014) 291-355]. We then show there is an equivalence of categories between them if σ = 0. We use this equivalence to better understand the action of the Lie superalgebra gl(1|1) on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and the second author in [An action of gl(1|1) on odd annular Khovanov homology, Math. Res. Lett. 27(3) (2020) 711-742].

Original languageEnglish (US)
Article number2450025
JournalJournal of Knot Theory and its Ramifications
Volume33
Issue number8
DOIs
StatePublished - Jul 1 2024

Keywords

  • Annular Khovanov homology
  • Lie superalgebra
  • odd Bar-Natan category

ASJC Scopus subject areas

  • Algebra and Number Theory

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