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nLab > Latest Changes: Tambara-Yamagami category

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1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthorperezl.alonso
    • CommentTimeFeb 23rd 2023

    Added definition of Tambara-Yamagami (TY) fusion category, the simplest example of non-invertible symmetries in the 2d defect language.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2023

    Hi Alonso, that’s great! I have added some more hyperlinks to technical terms (e.g. graded vector space) and I have touched the formatting and hyperlinking of the reference item (here)

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorsachin.valera
    • CommentTimeApr 28th 2023
    • (edited Apr 28th 2023)

    Edits: 1. Corrected Ug to Um on right-hand side of second and third fusion rules. 2. Added to properties: (1) Remark: G must be abelian and TY(G) not unique; (2) Proposition: TY(G) is unitary; (3) Proposition: TY(G) braided iff G≅ℤn2. 3. Added some examples. 4. Clarified ground field in article + added reference to categorification of TY fusion ring over reals.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorperezl.alonso
    • CommentTimeAug 21st 2023

    corrected an incorrect statement that TY(Z2xZ2) is (only) the category of representations of the dihedral group.

    diff, v6, current

    • CommentRowNumber5.
    • CommentAuthorsachin.valera
    • CommentTimeOct 15th 2024

    Edited example 1: relation of braided TY(Z_2) to Ising categories and representation category SU(2)_2

    diff, v7, current

    • CommentRowNumber6.
    • CommentAuthorperezl.alonso
    • CommentTimeMar 20th 2025

    Recording this paper from last night for later

    • Adrià Marín-Salvador. Continuous Tambara-Yamagami tensor categories (2025). (arXiv:2503.14596).

    I’m not adding it to the nLab entry yet since I don’t have time right now to go through the paper (plus some additional words would be required, as I can already see physicists using this pretending “continuous” = “smooth”, but that’s a different issue…).

1 to 6 of 6

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