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 Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли
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