Уваров Ф.В. - Группы и Алгебры Ли - 3. Homomorphism theorem and introduction to Lie algebra

00:00:14 Reminder of the previous lecture 00:02:07 Definition 1: immersed submanifold 00:06:16 Proposition 1: connection of a lie group action with an immersed submanifold 00:08:37 Proof of the proposition 1 00:20:37 Definition 2: virtual Lie subgroups 00:22:43 Examples of virtual Lie subgroups 00:24:50 Theorem 1: Homomorphism theorem 00:27:48 Proof of the theorem 1 00:31:07 Examples of the theorem 1 00:33:44 Definition 3: homogeneous space 00:37:09 Examples of homogeneous space 00:39:04 Definition 4: Lie algebra 00:44:36 Proposition 2: constant, linear and quadratic term 00:47:20 Proof of the proposition 2 00:49:55 Definition 5: Lie bracket 00:54:13 Proposition 3: Lie bracket doesn’t depend on the chart 00:55:28 Proof of the proposition 3 01:11:58 Example of a Lie bracket (GL_n) Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли