I'm having trouble getting my head arround the concept. Can someone explain it to me?
What is a Lie Group in layman's terms?
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lie-groups
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15As someone on mathoverflow asked: could you provide some context? What's your background? – 2011-02-20
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15My rule of thumb here is that you should read the Wikipedia article (http://en.wikipedia.org/wiki/Lie_group) and then ask about anything that confuses you in it. (This could be "all of it," which is fine. The important thing is that you should answer at least two other questions first: do you know what a group is, and do you know what a smooth manifold is?) – 2011-02-20
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13Never mind addressing the whole Wikipedia article, I think this question would be greatly improved by addressing the following question. In what way is the answer *"A smooth manifold with a group structure so that the group operations are smooth maps"* insufficient? Are you having trouble getting your head around this definition, around some particular examples, or around something else (like structure theory or the relationship with Lie algebras)? – 2011-02-20
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6Perhaps the correct questions are: Why should I care about Lie groups? What are they useful for? Why were they "invented"? What do they represent? An answer of the genre "a smooth manifold +++" is just not interesting from this perspective; I could make up lots of sets of axioms, but why do people care about this specific one? – 2011-02-21
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1My guess is that Lie groups are one of two frameworks in which it makes sense to study matrix groups, in particular it is well suited for studying these groups' topology and differential geometry of their homogeneous spaces. – 2012-10-27