

Mathoverflow: Fundamental Examples - Maro
http://mathoverflow.net/questions/4994/fundamental-examples

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lmkg
Looking over those examples, I would have to say hammer home how "fundamental"
is a very relative term. _su_3_ is mentioned as a fundamental example of a Lie
algebra, but it's not a fundamental example in, say, abstract algebra, even
though they can be an object of study in that domain. Perhaps Lie alebras are
themselves less fundamental than abstract algebra... then again, perhaps
they're more fundamental.[1]

I really like the idea of the site. My fear is that it gets bogged down around
semantics of "fundamental." You can split hairs over the differences between a
fundamental example, a seminal example, and a classic textbook example if you
want, but for the purpose of the site I'd rather have all of the above,
possibly categorized by tags.

[1] For the uninitiated: A Lie alebra is a set that has the structure of a
group (from abstract algebra) as well as the structure of a topological space,
in a way that the two structures are compatible. Even if you don't know what
these voodoo majicks are, you can still appreciate the conundrum: are groups
and topologies fundamental, and Lie algebras a Frankenstein's monster of math;
or are Lie algebras fundamental, and groups & topologies the result of
discarding information? I'm given to understand physics makes heavy use of Lie
algebras, somewhere, if that makes a difference.

~~~
andreyf
I'm not sure if "fundamental" makes much sense in relation to Lie groups.
There are a lot of sets out there. Some of them are groups, others are
topologies. Some are both. Similarly, there are people who have drivers
licenses, and there are people who have blue eyes. Then there are people who
have both blue eyes and drivers licenses. Those people are like lie groups.

