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Math Help - Paper Introducing Lie Algebras

  1. #1
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    Paper Introducing Lie Algebras

    Hello! I've written a paper for a class and if anyone had the time to glance it over and had any suggestions or notices any glaring errors, it would be great to hear any feedback!

    I pondering putting this in "Pre-prints and other original work" section of the forum but I thought this might be a better place, given that it's all just basic stuff about Lie algebras, nothing too tough or "original" work. Hopefully this is OK!

    Thanks for the reads, anyone who has a chance.
    Attached Thumbnails Attached Thumbnails Paper Introducing Lie Algebras-introduction-lie-algebrasmarch28.pdf  
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  2. #2
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    Ado's theorem and its generalization holds for a "finite dimensional" Lie algebra L only, i.e. L, as a vector space, must be finite dimensional.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by matt.qmar View Post
    Hello! I've written a paper for a class and if anyone had the time to glance it over and had any suggestions or notices any glaring errors, it would be great to hear any feedback!

    I pondering putting this in "Pre-prints and other original work" section of the forum but I thought this might be a better place, given that it's all just basic stuff about Lie algebras, nothing too tough or "original" work. Hopefully this is OK!

    Thanks for the reads, anyone who has a chance.
    Except for the one mentioned by NonCommAlg at least all the theorem statements look to be correct. Also, as a notational convention I would tend to, in accordance with the usual notation, use lower case mathfrak letters to denote algebras (i.e. \mathfrak{gl}(V) instead of \text{gl}(V)). This isn't a huge deal but it would be nice so that someone never seeing lie algebras before (since this introduction) wouldn't (even though you told them) not confuse say the space of tracless complex matrices \mathfrak{sl}\left(n,\mathbb{C}\right) with the special linear group.
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    Thank you very much for reading it over, Drexel and NonCommAlg. Much appreciated!
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