group theory questions

[tiger_striped_cat]

Anyone want to try and explain IN WORDS (try not to use any math symbols). If you have to use symbols, try and dumb it down further. Like:

A group is a mathematical object that satisfies four conditions that are:....

Can you define:

1. Lie Group
2. Lie Algebra
3. Representation
4. Roots
5. Weights

Thanks!