I was just wondering if anyone had any suggestions of more-mathematically-rigorous textbooks on Lie groups and Lie algebras for (high-energy) physicists than, say, Howard Georgi's book.
I have been eying books such as "Symmetries, Lie Algebras And Representations: A Graduate Course For Physicists" by J. Fuchs and C. Schweigert and "Lie Groups, Lie Algebras, and Some of Their Applications'' by R. Gilmore; however, the problem that arises with those, and with pure mathematical books on the subject, is that their (exponential map) convention is different from that used in physics: in physics, the Lie algebra of a matrix Lie group, G, is defined to be the set of all matrices X such that exp[itX] is in G for all real numbers t, whereas in math, the Lie algebra of G is defined by exp[tX], without the i. This leads to different conventions/results throughout the entire subject (for instance, the Lie algebra of the unitary group is the space of all hermitian matrices in physics, but the space of all ANTI-hermitian matrices in math -- it is obvious why the former convention is chosen in physics).
Even though the two textbooks that I listed above are meant for physicists, they have adopted the mathematical convention (I guess that is in line with their intent to be more mathematically rigorous), so I would like to look elsewhere, if possible.
So, just to summarize (since this post has become rather long -- sorry about that!): I am looking for a mathematically-rigorous textbook on Lie groups and Lie algebras that uses physicists' conventions.
I greatly appreciate your help!