By Mark R. Sepanski

Blending algebra, research, and topology, the examine of compact Lie teams is likely one of the most lovely components of arithmetic and a key stepping stone to the speculation of common Lie teams. Assuming no earlier wisdom of Lie teams, this e-book covers the constitution and illustration conception of compact Lie teams. insurance contains the development of the Spin teams, Schur Orthogonality, the Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus Theorem, the Commutator Theorem, the Weyl Integration and personality formulation, the top Weight type, and the Borel-Weil Theorem. The ebook develops the required Lie algebra concept with a streamlined strategy concentrating on linear Lie groups.

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