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nLab > Latest Changes: Kac-Moody algebra

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    I have half-heartedly started adding something to Kac-Moody algebra. Mostly refrences so far. But I don’t have the time right now to do any more.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    I have created the related entry affine Lie algebra. I think Kac-Moody Lie algebra should focus on general theory and references and examples for nonaffine case. Affine case is the main case in (geometric and physical) applications and we will undoubtfully have much about it, so it deserves to have its own entry. However I see now that there is an overlap with the existing entry current algebra.

    BTW, I do not feel strongly about it, but I think that the general convention was that the default name is the full name, so tangent Lie algebroid rather than Lie algebroid, Hausdorff topological space rather than Hausdorff space and then I guess Kac-Moody Lie algebra rather than Kac-Moody algebra, though all those cases are usually correct to refer both ways.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2012

    Hi Zoran,

    yes, I fully agree. I had similar thoughts already. But didn’t find the leisure to implement them.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2012
    • (edited Feb 8th 2012)

    It may make sense to keep current algebra a separate entry from affine Kac-Moody Lie algebra, I suppose. The former term alludes more to the fact that one thinks of vertex operator algebras and CFT, while the latter is more the purely Lie algebraic concept. Roughly.

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeFeb 8th 2012

    Right, I am not completely sure (current algebra vs. affine Lie algebra), the flavour and literature is a bit separated and the terminology also changed from 1960s when current algebra could also mean classical and quantum (like with or without the central charge). But I am not an expert on this terminology. In any case, someone competent should decide how to explain the terminology and cross-link accordingly.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJan 20th 2023

    Added higher Kac-Moody algebra as a related concept. Since this now clashes with

    The higher Kac-Moody analogs of the exceptional semisimple Lie algebras E7, E7, E8 are…

    I have rewritten as

    The sequence of exceptional semisimple Lie algebras E7, E7, E8 may be continued to the Kac-Moody algebras:

    diff, v13, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2024

    added pointer to

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2024

    added pointer to:

    diff, v21, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2024

    fixed several links

    diff, v22, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 8th 2024

    added the definition (here)

    diff, v23, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 9th 2024

    added definition of the maximal compact (involutory) subalgebra (here)

    diff, v24, current

1 to 11 of 11

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