zlacker

Probably the best place to get started with Lie groups is to wrap your head around SO(n), which has both a nice geometric interpretation as rotations of n-dimensional space as well as a concrete representation as the space of orthogonal (determinant 1) nxn matrices. With a little matrix calculus you can work out what the tangent directions are at the identity matrix: they’re precisely the skew-symmetric matrices. This is the Lie algebra so(n). Where the Lie group consists of rotations, the Lie algebra consists of directions in which you can rotate something, or really velocities of rotation. This is why classical angular momentum is actually an element of a Lie algebra.

>>aesthe+(OP)
I’m sorry but you used so many big words so close together, I could find no purchase with the things I know. Perhaps you could tell me what was the problem that Lie groups are supposed to solve. I read something about an infinitely symmetric transformation- the rotation of a circle is a Lie group. But then what are all the letters about- the A,B,C etc all the way up to E 8. And why did it take 77 hours on the Sage supercomputer to solve E8.