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source: James Cook 2016年1月19日

Matrix Lie Groups

You might also call this a course in Naive Lie Groups. The focus is on matrix group examples and a minimum of background in topology and manifold theory is needed. In particular, we follow Stillwell's text "Naïve Lie Groups"

Matrix Lie Groups: Lecture 1 part 1: complex and quaternions 59:51 We are working through Stillwell's Naive Lie Groups. There is a second part to this.

Lecture 1 part 2: complex and quaternion 25:38

Lecture 2 part 1: more quarternions, group theory 59:51

Lecture 2 part 2: more quarternions, group theory 28:25

Feb 1, chapter 2 (part 1) 59:51

Feb 1, chapter 2 and isometries over R,C and H (part 2) 31:21

Feb 8, chapter 3 path connectedness for SO(n) and SU(2) (part 1) 59:51

Feb 8, chapter 3 path connectedness for SO(n) and SU(2) (part 2) 27:36

Feb 22, Lie Groups and tangent space at I (part 1) 59:51

Feb 22, Lie Groups and tangent space at I (part 2) 34:54

March 8, what is the logarithm (part 1) 59:51

March 8, what is the logarithm (part 2) 29:27

March 21, on the derivative of a homomorphism 30:27

March 30, adjoint and Lie Algebra (part 1) 59:51

March 30, adjoint and Lie Algebra (part 2) 32:01

April 4, Lie algebra example, 2nd order BCH (part 1) 59:51

April 4, Lie algebra example, 2nd order BCH (part 2) 25:49

April 11, BCH identity (part 1) 59:51

April 11, BCH identity (part 2) 18:56

April 18, calculation of BCH (part 1) 59:51

April 18, BCH calculation (part 2) 30:21

universal covers and Lie's Theorem, April 25 (part 1) 59:51

covering groups and Lie's Theorem, April 25 (part 2) 12:57

May 2, group orbits and homogeneous space (part 1) 59:51

May 2, group orbits and homogeneous space (part 2) 36:08

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