# Lie Groups lecture 5

This lecture ( lie5 ) was given on 9/10/09

### Excerpts

One of the main things we did was prove the

Lie Product Formula: For

sketch of proof: prove prop. 2.8 in Brian Hall’s book that says if then . Worrying only about terms of order , we get so for large m apply the proposition

as m goes to infinity, the error term goes to zero.

Next we proved a big result that says every 1-parameter subgroup ( that is matrix lie group homo.) is of the form for some .

Using this, and the fact that (which can be proved by reducing to the Jordan Normal form (since conjugation doesn’t change det) and that splits X into commuting parts so effectively .) We classified various lie algebras.

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- Published:
- September 13, 2009 / 4:50 pm

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- Lie Groups (course)

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