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nLab > Latest Changes: Schur's lemma

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 24th 2018
    • (edited Sep 24th 2018)

    did some substantial edits on this entry:

    • gave it more of an Idea-section,

    • tried to streamline the statement of the lemma

    • spelled out the proof,

    • added a discussion explaining how this is about irreps forming a (de-)categorified orthogonal/orthonormal linear basis of the representation ring.

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2018
    • (edited Oct 1st 2018)

    slightly expanded the section on Generalizations and variants:

    Made the pointer to Schur’s lemma for simple objects in abelian categories more recognizable, and added pointer to Schur’s lemma for Bridgeland-stable objects

    diff, v11, current

    • CommentRowNumber3.
    • CommentAuthorGuest
    • CommentTimeMar 4th 2021
    Guest post: the characteristic 0 hypothesis seems to be unnecessary. See https://math.stackexchange.com/questions/3274435/a-corollary-of-schurs-lemma-in-positive-characteristic. --Max Weinreich
    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 5th 2021

    This was added in Revision 8 by Urs Schreiber on September 24, 2018 at 11:38:27.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 5th 2021

    And he removed it in rev 12. Hereby.

    Thanks for the heads-up. I forget why I went to put that condition in.

    diff, v12, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMar 5th 2021

    Slightly tweaked text and formatting of formulas at various places, for beautification.

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorJohn Baez
    • CommentTimeSep 7th 2023

    Added links to proof of Schur’s lemma for abelian categories.

    diff, v16, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2024

    added pointer to:

    diff, v18, current

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeJun 10th 2024

    Added

    and any non-zero morphism among isomorphic irreducibles is an isomorphism

    into idea part 1, as this is the important part of the content of Proposition 2.1.

    diff, v19, current

1 to 9 of 9

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