About Book
(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semi simple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skew symmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = – J MT with a certain non-degenerate skew symmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the “exceptional Lie 4 6 7 s algebras” , that just somehow appear in the process). There is also a discussion of the compact form and other real forms of a (complex) semi simple Lie algebra, and a section on auto morphisms. The third chapter brings the theory of the finite dimensional representations of a semi simple Lie alge bra, with the highest or extreme weight as central notion
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