Topic: Lie Groups & Lie Algebra

[Astronuc]

A nice intro to Lie Groups

http://en.wikipedia.org/wiki/Lie_group

http://mathworld.wolfram.com/LieGroup.html

 :koala

[remcook]

funny you should post that. Never heard of it and now this is on the BBC:

http://news.bbc.co.uk/1/hi/sci/tech/6466129.stm

can't say it makes much sense to me though.

[Astronuc]

Many of us in science and engineering may use Lie groups without realizing it.

I came across the subject about 30 years ago during my earliest years at university, and had planned to pursue study of Lie groups and algebras, but I got distracted and went in another direction.  Abstract algebra was never an big interest - but then perhaps if someone had shown me soon enough, I might have gotten interested.

I had also wanted to study nonlinear mathematics, but at the time I had the interest and energy, there were no courses.

[remcook]

could you give a simple example?

[Astronuc]

The wikipedia article gives several examples -

Invertible 2x2 matrices - http://en.wikipedia.org/wiki/Lie_group#Example

The group GL_n(R) of invertible matrices (under matrix multiplication) is a Lie group of dimension n² - http://en.wikipedia.org/wiki/General_linear_group

I definitely need to study up on this subject.

[remcook]

I can read those words, but they do not mean anything to me...those pages suffer from A LOT of jargon. even if i click on all the definnitions, it doesn't make much sense. maybe one needs the hardcore maths background to make any sense of it, but I doubt it... maybe i'll try and find a more layman's page...