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Published online by Cambridge University Press: 05 June 2012
The following notes on Lie Algebras and Root Systems follow fairly closely the lectures I gave on this subject at the Lancaster meeting, although more detail has been included in a number of places. The aim has been to give an outline of the main ideas involved in the structure and representation theory of the simple Lie algebras over ℂ, and the construction of the corresponding groups of Lie type over an arbitrary field.
It has not been possible to give all the proofs in detail, and so interested readers are encouraged to consult books in which more complete information is given. The following books are particularly recommended.
J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics 9 (1972) Springer.
N. Jacobson, Lie Algebras. Interscience Publishers, J. Wiley, New York (1962).
R. W. Carter, Simple Groups of Lie Type, Wiley Classics Library Edition (1989), J. Wiley, New York.
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