Freudenthal-weil theorem for arbitrary embeddings of connected lie groups in compact groups

Advanced Studies in Contemporary Mathematics (Kyungshang)

Volumn 19, Issue 2, 2009, Pages 157-164

  Shtern, Alexander I ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

MAP group; Freudenthal Weil theorem; Locally compact group; Semisimple compact group

Indexed keywords

EID: 70350345355     PISSN: 12293067     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. H. Freudenthal, Topologische Gruppen mit genugend vielen fastperiodischen Funktionen, Ann. of Math. 37 (1936), 57-77.
2. A. Weil, L'intégration dans les groupes topologiques et ses applications, 2nd ed., Act. Sc. Ind. No.1145, Hermann, Paris, 1953.
3. A. I. Shtern, Freudenthal- Weil theorem for not necessarily continuous embeddings in compact groups (to appear).
4. A. I. Shtern, Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjecture, Adv. Stud. Contemp. Math. (Kyungshang) 13 (2006), no.2, 143-158.
5. A. I. Shtern, Analog of van der Waerden's continuity theorem and the validity of Mishchenko's conjecture for relatively compact homomorphisms of arbitrary locally compact groups, Adv. Stud. Contemp. Math. (Kyungshang) 14 (2007), no.1, 1-20.
6. A.I. Shtern, A version of the van der Waerden theorem and the proof of the Mishchenko conjecture for homomorphisms of locally compact groups, Izv. Ross. Akad. Nauk Ser. Mat. 72 (2008), no.1, 183-224
7. English transl.: Izv. Math. 72 (2008), no.1, 169-205.
8. A. I. Shtern, Finite-dimensional locally bounded quasirepresentations of connected locally compact groups: a survey, Adv. Stud. Contemp. Math. (Kyungshang) 19 (2009), no.1, 1-16.
9. B. L. van der Waerden, Stetigkeitssätze für halbeinfache Liesche Gruppen, Math. Z. 36 (1933), 780-786.
10. W. Banaszczyk, Additive subgroups of topological vector spaces 1991. (Lecture Notes in Math. V. 1466.) Springer-Verlag, Berlin.
11. V. S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1974.
12. C. C. Moore, Groups with finite dimensional irreducible representations, Trans. Amer. Math. Soc. 166 (1972), 401-410.
13. L. C. Robertson, A note on the structure of Moore groups, Bull. Amer. Math. Soc. 75 (1969), 594-599.
14. A. I. Shtern, Locally bicompact groups with finite-dimensional irreducible representations, Mat. Sb. 90 (1973), no.1, 86-93.
15. A. I. Shtern, Topological groups with finite group von Neumann algebras of type I, Mat. Sb. (new ser.) 196 (2005), no.3, 143-160
16. English transl.: Sb. Math. 196 (2005), no.3, 447-463.
17. A. I. Shtern, Compact semitopological semigroups and reflexive representability of topological groups, Russ. J. Math. Phys. 2 (1994), no.1, 131-132.
18. A. I. Shtern, A criterion for a topological group to admit a continuous embedding in a locally compact group, Russian Journal of Mathematical Physics 15, no.2, 297-300.
19. K. H. Hofmann, S. A. Morris, The Structure of Compact Groups, de Gruyter, Berlin, 1998.
20. N. Bourbaki, Éléments de mathématique. Fascicule XXIX. Livre VI: Intégration. Chap. 7 et 8, Hermann, Paris, 1963.
21. K. Iwasawa, On some types of topological groups, Ann. of Math. 50 (1949), 507-558.
22. A. I. Shtern, Almost periodic functions and representations in locally convex spaces, Uspekhi Mat. Nauk 60 (2005), no.3, 97-168
23. English transl.: Russ. Math. Surv. 60 (2005), no.3, 489-557.