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- Thread starter waht
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George Jones

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Tough question.

How much rigor?

Are you interested because of the beautiful math?

Because of applications to elementary particles and quantum field theory?

Just Lie groups and Lies algebras, or representations, too.

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Here's his paper: http://arxiv.org/abs/0711.0770

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The main problem that's foxing me with them at the moment, and I'd like to find a good answer for, is why it's the commutation relations that are fundamental and not the operators themselves.

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George Jones

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"[URL [Broken]Just pure maths, grad or undergrad, but rigor not blown out of proportions. My end goal is to understand E8, and see what's it all about.

Semi-Simple Lie Algebras and their Representations[/URL] by Robert Cahn is a free book (wasn't free when I picked it up!) on Lie algebras that has a chapter on the exceptional algebras. This book was written for physicists, but doesn't refer to any physics applications.

"[URL [Broken]

Representation Theory: A First Course[/URL] by Fulton and Harris, a standard math text, starts off terse, but becomes very readable and (maybe too) expansive in its middle. It's cool to see quark multiplet diagrams (as representations of [itex]sl\left(3 , \mathbb{C}\right) \cong \mathbb{C} \otimes su\left(3\right)[/itex]) appearing in a pure math book, even though the book doesn't identify them as such.

I have never really looked at the representations of the exceptional Lie algebras, so I can't comment on the treatment in either book.

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Yes, I'm familiar with this paper, it's the main reason why I want to learn all the Lie stuff.I would also like to learn about Lie Algebra for the same reason as waht. E8 seems very interesting and Lie Algebra just seems so fundamental for quantum field theory. A great tool to have, but how should one learn it? Waht, have you checked out Lisi's paper, "An Exceptionally Simple Theory of Everything?" I am having trouble understanding much of anything from it, and I think learning Lie Algebra would be a great start.

Thanks George, that's an excellent book on Lie Algebra, already learned something at first glance."[URL [Broken]

Semi-Simple Lie Algebras and their Representations[/URL] by Robert Cahn is a free book (wasn't free when I picked it up!) on Lie algebras that has a chapter on the exceptional algebras. This book was written for physicists, but doesn't refer to any physics applications.

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I am actually having trouble viewing this book. What do I need in order to view it?

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CompuChip

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http://pages.cs.wisc.edu/~ghost/

GPL Ghostscript 8.61 and AFPL Ghostscript

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CompuChip

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http://www.ps2pdf.com/

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