Уваров Ф.В. - Группы и Алгебры Ли - 14. Solvable Lie algebra, Lie theorem

00:00:14 Plan of the lecture
00:00:45 Definition 1: An ideal
00:05:00 Definition 2: A commutant of two ideal
00:06:14 Definition 3: A derived series
00:08:55 Lemma 1: Lie algebra quotient with a derived series is abelian
00:10:03 Proof of lemma 1
00:12:19 Definition 4: Solvable algebra
00:13:12 Proposition 1: criterion of solvability
00:16:17 Proof of the proposition 1
00:21:10 Definition 5: a flag
00:22:37 Proposition 2: "b" of a full flag is solvable
00:24:44 Proof of the proposition 2
00:32:31 Proposition 3: if Lie algebra quotient with an ideal is solvable, then Lie algebra is solvable
00:33:41 Proof of the proposition 3
00:36:20 The first Lie's theorem
00:38:34 Proof of the first Lie's theorem
01:05:50 Corollary 1: Any irreducible representation of solvable Lie algebra is 1-dim
01:06:46 Proof of the corollary 1
01:07:40 Second Lie's theorem
01:09:09 Proof of the second Lie's theorem

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