Introduction to Lie groups and Lie algebras 1
By Mehdi Nadjafikhah (IUST)

References:
M. Nadjafikhah, An introduction to differentiable manifolds, IUST, 2017.
E.L. Mansfield, A Practical Guide to the Invariant Calculus, Cambridge University Press, 2010.
A. Razavi, Lie groups and Lie algebras, AUT, 2015.

Course materials:

No.	Contents	Text	Audio
01	introduction and motivations	T01	A01
02	topological groups	T02	A02
03	examples of topological groups, Lie groups	T03	A03
04	category of Lie groups	T04	A04
05	homogeneous spaces, Lie algebras	T05	A05
06	Lie algebra of a Lie group	T06	A06
07	examples of Lie algebra of a Lie group	T07	A07
08	one-parameter Lie groups	T08	A08
09	exponential map of Lie group	T09	A09
10	properties of exponential map and its relation to Lie groups	T10	A10
11	Maurer-Cartan form and its properties	T11	A11
12	examples of Maurer-Cartan forms, group actions	T12	A12
13	properties and examples of group actions	T13	A13
14	some structural theorems	T14	A14
15	introduction to invariant calculus and its applications	T15	A15
16	transformation groups, prolongation	T16	A16
17	transversality, infinitesimal prolongation	T17	A17
18	examples and main formula of prolongation	T18	A18
19	moving coframe and some examples	T19	A19
20	invariantisation map	T20	A20
21	computation by Maple	T21	A21
22	matrix curvature computations	T22	A22

Some Exams: Mid-term, Final

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