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nLab > Latest Changes: classical Lie groups

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2010
    • (edited Sep 19th 2010)

    created stubs classical Lie group and exceptional Lie group and linked to them from simple Lie group (all very stubby)

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeSep 19th 2010

    [exception al Lie group]?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2010

    thanks, fixed.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeSep 20th 2010

    I do not think that by the classical Lie groups one means only classical simple Lie groups, but at least also the GL(n) which is not simple but reductive. One also says expression classical groups meaning not only the Lie versions over reals and complexes but also the same series over other fields as algebraic groups.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2010

    On Wikipedia they say something like “from a modern perspective GL(n) is the most classical of all Lie groups, but it does not count as classical in the classical sense “.

    But, yeah, I suppose the main point is that the entry should eventually give a much more in-depth discussion, either way.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeSep 21st 2010

    All the people who do "representations of classical groups" whom I know do count GL(n).

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeSep 22nd 2010

    I added to classical Lie group that other matrix Lie groups may count as classical.

    But we also have matrix Lie group, which seems to be the meaning that Zoran espouses. Maybe we should rename classical Lie group to classical simple Lie group?

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeSep 22nd 2010

    No, I think it is OK as it was (I mean title does not need to say simple, while it can be a redirect) as long as it has remark that at least GL(n) also counts. As far as the name of the page I like "classical group" as it does not put Lie group aspect in front of algebraic group aspect. IN the literature different people take different viewpoint but certainly other fields should be allowed.

1 to 8 of 8

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