Lie Algebra Book with Examples

Question

Can any body suggest me some text books or Lecture notes on Lie algebra and its representation theory which explains the concepts through 'lots' of examples?

Thanks in advance.

Answer 1

The typical book people use for examples is Fulton and Harris, which contains numerous graphs and explicit constructions for low dimensional Lie algebras. For example you can find the weight diagram of $sl_{4}\mathbb{C}$ explicitly in the book. My guess is since they did the job so well, others do not bother to write a similar book. But maybe I am wrong(as the comments showed).

For a really low-level introduction on Lie group/algebra with concrete examples and computations, you can use Brian Hall's book. But this book has much less material than Fulton and Harris, such that after one month of my undergraduate research I found I know everything in the book already by working on my own. I cannot say the same for Fulton and Harris.