Weblectures Lie Groups 2012, University of Utrecht

Welcome to the website on which the weblectures of the Master's course Lie Groups are available. The course was given by prof. dr. Erik van den Ban at the University of Utrecht in the spring of 2012.

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Lie Groups

Date Lecture Covered material
Feb 15th Lecture 1 - part 1
Lecture 1 - part 2		 Section 2: Lie groups: definition and basic properties.
Feb 22nd Lecture 2 - part 1
Lecture 2 - part 2		 Section 3: invariant vector fields, the exponential map; Section 4: the Lie algebra of a Lie group, up to Lemma 4.9.
Feb 29th Lecture 3 - part 1
Lecture 3 - part 2		 Rest of section 4; Section 5: commuting elements, component of the identity.
Mar 7th Lecture 4 - part 1
Lecture 4 - part 2		 Section 6: commutative Lie groups; Section 7: Lie subgroups, except for the proof of Lemma 7.7: the Lie algebra of a Lie subgroup.
Mar 14th Lecture 5 - part 1
Lecture 5 - part 2		 Proof of Lemma 7.7: the Lie algebra of a Lie subgroup; Section 9: closed subgroups; Section 10: the groups SU(2) and SO(3).
Mar 21st Lecture 6 - part 1
Lecture 6 - part 2		 Section 10: the groups SU(2) and SO(3), completion; Section 11; Section 12: Lemma 12.4, the uniqueness part of theorem 12.5.
Mar 28th Lecture 7 - part 1
Lecture 7 - part 2		 Sections 12, 13, 14, 16, 17.
Apr 4th Lecture 8 - part 1
Lecture 8 - part 2		 Few comments on section 15; part of section 19.
Apr 11th Lecture 9 - part 1
Lecture 9 - part 2		 Section 19 and part of section 20.
Apr 18th Lecture 10 - part 1
Lecture 10 - part 2		 Sections 20, 21, 23.
Apr 25th Lecture 11 - part 1
Lecture 11 - part 2		 Sections 22, 26, 27.
May 2nd Lecture 12 - part 1
Lecture 12 - part 2		 Sections 29, 30 and part of section 31.
May 9th Lecture 13 - part 1
Lecture 13 - part 2		 Sections 31-35.
May 16th Lecture 14 - part 1
Lecture 14 - part 2		 Sections 33, 34 and 36 up to Proposition 36.6.
May 23rd Lecture 15 - part 1
Lecture 15 - part 2		 Sections 36, 37 and 38.1 up to Lemma 38.4.
May 30th Lecture 16 - part 1
Lecture 16 - part 2		 Sections 38.1, 38.2, 38.3 and 38.5.