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nLab > Latest Changes: group algebra

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2012
    • (edited Oct 14th 2012)

    the entry group algebra had been full of notation mismatch and also of typos. I have reworked it now.

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeDec 7th 2013

    I have added into group algebra a definition of the completed group algebra of a profinite group.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2021

    added statement and proof (here) that the complex group algebra of a finite group is isomorphic to the direct sum of linear endomrophism algebras of its complex irreps.

    diff, v21, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2023
    • (edited Jul 9th 2023)

    added pointer to

    for the case of locally compact topological groups

    diff, v24, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2023

    added pointer to:

    diff, v30, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2023
    • (edited Dec 2nd 2023)

    maybe this is the origin of the notion of group algebras:

    ?

    diff, v30, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2023

    added a (currently brief) paragraph (here) on group algebras of central extensions relating to twisted group algebras

    diff, v30, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeDec 3rd 2023
    • (edited Dec 3rd 2023)

    have spelled out (here) the case of complex group algebras of U(1)\mathrm{U}(1)-central extensions G ωG^\omega relating to ω\omega-twisted group algebras of GG.

    diff, v31, current

    • CommentRowNumber9.
    • CommentAuthorperezl.alonso
    • CommentTimeDec 3rd 2023

    just a minor note, twisted group algebras are in general not Hopf algebras anymore

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023

    added pointer to:

    (here and at strict deformation quantization)

    diff, v32, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023

    and pointer to

    (here and at groupoid algebra)

    diff, v34, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2023

    also pointer to:

    diff, v34, current

    • CommentRowNumber13.
    • CommentAuthorJ-B Vienney
    • CommentTimeJun 21st 2024

    Added that the group ring R[G]R[G] where GG is an abelian group and RR is a commutative ring is an integral domain iff RR is an integral domain and GG is torsion-free.

    diff, v37, current

  14. changed higher algebra - contents to algebra - contents in context sidebar

    Anonymouse

    diff, v39, current

    • CommentRowNumber15.
    • CommentAuthorTim_Porter
    • CommentTimeOct 17th 2024

    I searched for cocycle but typed in cocyle by error!!!…. and found there were several instances of that typo. I fixed a few on this page.

    diff, v40, current

1 to 15 of 15

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