LECTURE NOTES

  • Lecture 1
    History. Examples. Definitions. **** not written yet **

  • Lecture 2
    Getting the Lie algebra from the group.

  • Lecture 3
    The exponential map: from the algebra back to the group.

  • Lecture 3 A
    Loose end: the bracket in the matrix case

  • Lecture 4
    Functorial equivalence. Simply connected Lie groups.

  • Lecture 5
    The three adjoint actions.

  • Lecture 6
    Differential of the exponential map ( 1/19 and 1/24)..

  • Lecture 6A
    Characterizing connected Abelian Lie groups ( 1/19)..

  • Lecture 7
    universal covers. fundamental group. ( Andrew Marshall speaks )..

  • Lecture 8?
    Characterizing simply connected Nilpotent Lie groups ( 1/31 ?)..

  • Lecture 9
    universal cover of a Lie group is Lie

  • Lecture 9A
    Exponentiating algebra homomorphisms to the group; subalgebra-subgroup theorem. ( 1/31 ?)..

  • Lecture 11
    `Chapter 2': goal : get to Cartan's classification of compact Lie groups.

  • Lecture 11 + N
    the dual perspective. preparation for Koiller's lecture of Feb 23
  • G2 and rolling
    a ROUGH draft of a paper w Gil Bor

  • Geometry on Lie Groups; Maximal Torus proof.
    last TeXed lecture