The action of a semisimple lie group on its maximal compact subgroup
Proceedings of the American Mathematical Society, cilt.129, sa.5, ss.1525-1534, 2001 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 129 Sayı: 5
- Basım Tarihi: 2001
- Doi Numarası: 10.1090/s0002-9939-01-05984-6
- Dergi Adı: Proceedings of the American Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1525-1534
- Boğaziçi Üniversitesi Adresli: Evet
Özet
In this paper we determine the structure of the minimal ideal in the enveloping semigroup for the natural action of a connected semisimple Lie group on its maximal compact subgroup. In particular, if G = KAN is an Iwasawa decomposition of the group G, then the group in the minimal left ideal is isomorphic both algebraically and topologically with the normalizer M of AN in K. Complete descriptions are given for the enveloping semigroups in the cases G = SL(2, ℂ) and G = SL(2, ℝ). © 2001 American Mathematical Society.