# LECTURE NOTES

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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