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Mathoverflow: Fundamental Examples
- lmkg 17y agoLooking 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 17y agoI'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.