Complex semi-simple Lie algebras and their representations

under construction

In this course we learn the basics of w:complex semi-simple Lie algebras.

Why? edit

  • the classification of compact Lie groups reduces to the classification of semi-simple Lie algebras
  • the key notion of a root system reappears in many branches of mathematics and theoretical physics
  • Lie algebras and their representations are intimately related to quantum mechanics

some references edit

on paper edit

In increasing order of details:

  • J.-P. Serre, Complex semi-simple Lie algebras (translated from French: Algebres de Lie complex semi-simple
  • J. E. Humphreys, Introduction to Lie algebras and representation theory , ISBN 978-0-387-90053-7
  • W. Fulton, J. Harris, Representation theory, A first course

on line edit

There is plenty of lecture notes and other good references on line to suit every taste.

lessons edit

tests edit

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examination edit

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beyond edit