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nLab > Latest Changes: quantum Yang-Baxter equation

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  1.  

  1. Update the link to Drinfeld’s paper (pdf).

    Anonymous

    diff, v4, current

  2. Statement with multiplicative spectral parameter

    Ammar Husain

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2022

    Entry improved.

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeSep 2nd 2022

    It is a little bit awkward that the entry is called quantum Yang-Baxter matrix with redirect quantum Yang-Baxter equation, but the matrix case is just a special case in the category of vector spaces. Maybe we should split the entry or simply do it other way around, making the title quantum Yang-Baxter equation and then having a special case mentioned as a redirect. This is far more logical.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2022

    fixed typos (brading, categores)

    inserted missing “the”s

    fixed formatting of math formulas

    fixed “the quantum YB operator” to “a quantum YB operator”

    added hyperlinks to the main technical terms

    added cross-link with braid group representation

    added a pointer on the use of qYB for braid group representations:

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2022
    • (edited Dec 26th 2022)

    am renaming the entry from “quantum Yang-Baxter matrix” to “quantum Yang-Baxter equation”

    diff, v9, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2022
    • (edited Dec 26th 2022)

    I have turned the remark “Historical motivation” from a sub-subsection into a Remark (now here).

    (This remark would be more useful if it provided any reference for its claims.)

    diff, v9, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2022

    added pointer to the original references that the historical remark means to refer to:

    diff, v10, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 26th 2022
    • (edited Dec 26th 2022)

    added pointer to:

    • Michio Jimbo, Introduction to the Yang-Baxter Equation, Int. J. Modern Physics A 4 15 (1989) 3759-3777 [doi:10.1142/S0217751X89001503]

      reprinted in: Braid Group, Knot Theory and Statistical Mechanics, Advanced Series in Mathematical Physics 9, World Scientific (1991) [doi:10.1142/0796]

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2022

    Changed

    into

    • categories of representations of quantum groups; often (a completion of) a quantum group GG itself has a particular element ℛ\mathcal{R}, called a universal ℛ\mathcal{R}-element, satisfying axioms (quasitriangularity) ensuring that its image in every representation satisfies qYBE

    diff, v11, current

1 to 10 of 10

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