Уваров Ф.В. - Группы и Алгебры Ли - 1. Lie groups and subgroups

00:00:14 Short description of the course 00:00:23 Definition 1: Lie group 00:04:51 Examples of Lie groups 00:10:25 Definition 2: Lie subgroup 00:11:51 Definition 3: submanifold 00:15:24 Different examples 00:24:19 Proposition 1: criterion of finding a submanifold 00:27:17 Proof that SL_n is a Lie subgroup of GL_n 00:33:40 Proposition 2: if H is a Lie subgroup, then H is closed 00:35:37 Proof of the proposition 2 00:42:25 Definition 3: homomorphism of Lie groups 00:44:28 Examples of homomorphisms 00:46:54 Question: Are Image and Kernel Lie subgroups? 00:48:59 Definition 4: Lie group action 00:51:00 Examples of Lie group action 00:53:07 Theorem 1: if G - Lie group action, then stabilizer is a Lie subgroup 00:54:32 Proof of the theorem 1 01:02:13 Remark: knowing rank, we can compute dimention 01:03:32 Application of the theorem 1 Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли