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nLab > Latest Changes: Drinfeld center

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2013
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2013
    • (edited Apr 8th 2013)

    I have stated the relation

    Drinfeld double ↔\leftrightarrow Drinfeld center

    more explicitly in both entries (but still without any details).

    Then I made that a row in the table structure on algebras and their module categories - table

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeApr 8th 2013
    • (edited Apr 8th 2013)

    The canonical name is center of a monoidal category. Some recent articles started using the name “Drinfeld center” as it generalizes the Drinfeld double, in a sense, but the construction is due Shahn Majid and it has a relative version right away (see Majid’s Foundations book, chapter IX).

    Ross Street has a paper on realizing it as sort of a 2-categorical limit.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2013
    • (edited Apr 8th 2013)

    Redicrects are in place. If you feel the entry should be renamed, please do.

    The Street-reference I have included now. Too bad that this does not relate to the important characterization via “endomorphisms of the identity”. (Or maybe it’s implicit somewhere? I have only glanced over it.)

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeApr 8th 2013

    No, it is just a comment on the background.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2020

    added pointer to the recent

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeNov 10th 2021
    Hi, I believe Proposition 3.2 is incorrect in that generality. The categorical dimension of the center of C is the square of the categorical dimension of C, and it could very well happen that the latter is invertible in the ground field but the former is not. Then you should have a Maschke-type situation.

    Jo
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2021

    Thanks for the alert. I have added (here) the clause that the ground field be algebraically closed and of characteristic zero, and added pointer to proof, review and further references.

    There would be a lot more to be said, and in more generality. Please feel invited to edit.

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorperezl.alonso
    • CommentTimeSep 1st 2024

    very brief characterization of 𝒵(Vec G)\mathcal{Z} (Vec_G ) (mainly for reference)

    diff, v13, current

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