Уваров Ф.В. - Группы и Алгебры Ли - 13. Characters and Peter-Weyl theorem

00:00:14 Correction of previous mistakes 00:06:00 Definition 1: Characters of the representation 00:08:16 Lemma 1: Properties about characters 00:10:04 Proof of the lemma 1 00:17:50 Comments about irreducible complex representations 00:19:20 Proposition 1: Characters of irreducible complex representations 00:23:06 Proof of the proposition 1 00:26:57 Corollary 1: of the proposition 1 00:29:53 Proof of the corollary 1 00:36:33 Characters for sl(2) 01:00:30 Introduction to some things before Peter-Weyl theorem 01:10:17 Proposition 2: the map preserves inner product 01:11:45 Proof of the proposition 2 01:20:10 M preserves right and left actions 01:25:40 Proposition 3: M is a homomorphism of G-modules 01:26:12 Proof of the proposition 3 01:28:05 Peter-Weyl theorem 01:31:50 Remark 1 about Peter-Weyl theorem 01:34:30 Remark 2 about Peter-Weyl theorem 01:36:24 Plan for the next lecture and a question from the audience Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли