Continuity conditions for finite-dimensional representations of some locally bounded groups

Russian Journal of Mathematical Physics

Volumn 13, Issue 4, 2006, Pages 438-457

  Shtern, A I ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845622356     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: 10.1134/S1061920806040078     Document Type: Article

References (39)

1. S. Ahdout, C. Hurwitz, G. Itzkowitz, S. Rothman, and H. Strassberg, "Maximal Protori in Compact Topological Groups," in Papers on General Topology and Applications (Flushing, NY, 1992), Ann. New York Acad. Sci. 728 (New York Acad. Sci., New York, 1994), pp. 227-236.
2. W.W. Comfort and T. Soundararajan, "Pseudocompact Group Topologies and Totally Dense Subgroups," Pacific J. Math. 100 (1), 61-84 (1982).
3. W. W. Comfort, "Topological Groups," in Handbook of Set-Theoretic Topology (North-Holland, Amsterdam-New York, 1984), pp. 1143-1263.
4. W. W. Comfort and F. J. Trigos-Arrieta, "Locally Pseudocompact Topological Groups," Topology Appl. 62 (3), 263-280 (1995).
5. W. W. Comfort and J. van Mill, "Concerning Connected, Pseudocompact Groups," Topology Appl. 33 (1), 21-45 (1989).
6. D. M. Evans and P. R. Hewitt, "Counterexamples to a Conjecture on Relative Categoricity," Ann. Pure Appl. Logic 46 (2), 201-209 (1990).
7. V. M. Glushkov [Gluskov], "Structure of Locally Bicompact Groups and Hilbert's Fifth Problem," Uspekhi Mat. Nauk 12 (2), 3-41 (1957) [Amer. Math. Soc. Translations].
8. B. Hartley, "Subgroups of Finite Index in Profinite Groups," Math. Z. 168 (1), 71-76 (1979).
9. E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol. I (Springer, Berlin-New York, 1979).
10. K. H. Hofmann and S. A. Morris, The Structure of Compact Groups (de Gruyter, Berlin-New York, 1998).
11. E. Hotzel, "Maximality Properties of Some Subsemigroups of Baer-Levi Semigroups," Semigroup Forum 51 (2), 153-190 (1995).
12. E. Hotzel, "Right Projective Semigroups with 0," Pure Appl. Algebra 170 (1), 35-66 (2002).
13. S. N. Hudson, "On Connectivity Properties of Finite-Dimensional Groups," Proc. Amer. Math. Soc. 82 (2), 429-450 (1979).
14. K. Iwasawa, "On Some Types of Topological Groups," Ann. of Math. (2) 50 (3), 507-558 (1949).
15. S. Lang, Introduction to Diophantine Approximations (Addison-Wesley, Reading, Mass.-Palo Alto, London-Don Mills, Ont., 1966).
16. D. H. Lee, "Supplements for the Identity Component in Locally Compact Groups," Math. Z. 104 (1), 28-49 (1968).
17. D. Montgomery and L. Zippin, Topological Transformation Groups (Interscience, New York, 1955).
18. M. A. Naimark and A. I. Štern [Shtern], Theory of Group Representations (Springer, New York-Heidelberg-Berlin, 1982).
19. N. Nikolov and D. Segal, "Finite Index Subgroups in Profinite Groups," C. R. Acad. Sci. Paris, Sér. I 337, 303-308 (2003).
20. N. Nikolov and D. Segal, "On Finitely Generated Profinite Groups, I: Strong Completeness and Uniform Bounds," arXiv preprint:math.GR/0604399 (2006).
21. N. Nikolov and D. Segal, "On Finitely Generated Profinite Groups, II: Products in Quasisimple Groups," arXiv preprint:math.GR/0604400 (2006).
22. B. C. Oltikar and L. Ribes, "On Prosupersolvable Groups," Pacific J. Math. 77 (1), 183-188 (1978).
23. A. L. T. Paterson, Amenability (Amer. Math. Soc., Providence, 1988).
24. H. L. Peterson, "Discontinuous Characters and Subgroups of Finite Index," Pacific J. Math. 44 (2), 683-691 (1973).
25. A. Pletch, "Strong Completeness in Profinite Groups," Pacific J. Math. 97 (1), 203-208 (1981).
26. J. Saxl and J. S. Wilson, "A Note on Powers in Simple Groups," Math. Proc. Camb. Phil. Soc. 122 (1), 91-94 (1997).
27. D. Segal, "Closed Subgroups of Profinite Groups," Proc. London Math. Soc. (3) 81 (1), 29-54 (2000).
28. A. I. Shtern, "Quasirepresentations and Pseudorepresentations," Funktsional. Anal. i Prilozhen. 25 (2), 87-91 (1991).
29. A. I. Shtern, "Criteria for Weak and Strong Continuity of Representations of Topological Groups in Banach Spaces," Mat. Sb. 193 (9), 139-156 (2002)
30. [Sb. Math. 193 (9), 1380-1396 (2002)].
31. A. I. Shtern, "Continuity of Banach Representations in Terms of Point Variations," Russian J. Math. Phys. 9 (2), 251-253 (2002).
32. A. I. Shtern, "Continuity Criteria for Finite-Dimensional Representations of Compact Connected Groups," Adv. Stud. Contemp. Math. 6 (2), 141-156 (2003).
33. A. I. Shtern, "Continuity Conditions for Finite-Dimensional Representations of Some Compact Totally Disconnected Groups," Adv. Stud. Contemp. Math. 8 (1), 13-22 (2004).
34. A. I. Shtern, "Continuity Criteria for Finite-Dimensional Representations of Connected Locally Compact Groups," Mat. Sb. 195 (9), 145-159 (2004).
35. A. I. Shtern, "Van der Waerden's Continuity Theorem for Arbitrary Semisimple Lie Groups," Russian J. Math. Phys. 13 (2), 210-223 (2006) (http://www.springerlink.com/index/K2707W267T77064L.pdf).
36. 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. 13 (2), 143-158 (2006).
37. A. I. Shtern, "A Version of Serre's Problem and Continuity Conditions for Finite-Dimensional Representations of Topological Groups," Fund. Prikl. Mat., to appear (2007).
38. M. Stroppel, "Lie Theory for Non-Lie Groups," J. Lie Theory 4 (2), 257-284 (1994).
39. A. Weil, Sur les espaces à structure uniforme et sur la topologie générale, Publications Mathématiques de l'Université Strasbourg, fasc. II (Hermann & Cie, Paris, 1937).