Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The independence of characters on non-abelian groups

Authors: David Grow and Kathryn E. Hare
Journal: Proc. Amer. Math. Soc. 132 (2004), 3641-3651
MSC (2000): Primary 43A65; Secondary 43A46, 22E46
Published electronically: May 20, 2004
MathSciNet review: 2084087
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that there are characters of compact, connected, non-abelian groups that approximate random choices of signs. The work was motivated by Kronecker's theorem on the independence of exponential functions and has applications to thin sets.

References [Enhancements On Off] (What's this?)

  • 1. H. Bohr, Zur Theorie der Fast Periodischen Funktionen (I. Teil), Acta Math. 45 (1925), 29-127.
  • 2. H. Bohr, Almost periodic functions (Translated by H. Cohn), Chelsea Publishing Co., New York, 1947. MR 8:512a
  • 3. T. Bröcker and T. tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics, no. 98, Springer-Verlag, New York, 1985. MR 86i:22023
  • 4. T. Dooley, Central lacunary sets for Lie groups, J. Austral. Math. Soc. Ser. A 45 (1988), 30-45. MR 89j:43007
  • 5. P. Gallagher, Zeroes of group characters, Math. Z. 87 (1965), 363-364. MR 31:276
  • 6. K. Hare, The size of characters of compact Lie groups, Studia Mathematica 129 (1998), 1-18. MR 99c:43013
  • 7. K. Hare, Central Sidonicity for compact Lie groups, Ann. Inst. Fourier (Grenoble) 45 (1995), 547-564. MR 96i:43004
  • 8. K. Hare and D. Wilson, Weighted $p$-Sidon sets, J. Austral. Math. Soc. Ser. A 61 (1996), 73-95.MR 97j:43002
  • 9. S. Hartman and C. Ryll-Nardzewski, Almost periodic extensions of functions, Colloq. Math. 12 (1964), 23-39.MR 29:5057
  • 10. E. Hewitt and K. Ross, Abstract harmonic analysis II, Springer-Verlag, New York, 1970. MR 41:7378
  • 11. E. Hewitt and H. Zuckerman, A group theoretic method in approximation theory, Annals of Mathematics 52 (1950), 557-567. MR 12:801c
  • 12. J. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York, 1972. MR 48:2197
  • 13. J. Lopez and K. Ross, Sidon sets, Lecture Notes in Pure and Applied Math. 13, Marcel Dekker, New York, 1975. MR 55:13173
  • 14. W. Parker, Central Sidon and central $\Lambda _{p}$ sets, J. Austral. Math. Soc. 14 (1972), 62-74. MR 47:9178
  • 15. J. Price, Lie groups and compact groups, London Math. Soc. Lecture Note Series No. 25, Cambridge Univ. Press, Cambridge, 1977. MR 56:8743
  • 16. D. Ragozin, Central measures on compact simple Lie groups, J. Funct. Anal. 10 (1972), 212-229. MR 49:5715
  • 17. L. T. Ramsey, Comparisons of Sidon and $I_{0}$sets, Colloq. Math. 70 (1996), 103-132. MR 97m:43004
  • 18. D. Rider, Central lacunary sets, Monatsh. Math. 76 (1972), 328-338. MR 51:3801
  • 19. W. Rudin, Fourier analysis on groups, Interscience Publishers, New York, 1962. MR 27:2808
  • 20. B. Simon, Representations of finite and compact groups, Graduate Studies in Mathematics 10, Amer. Math. Soc., Providence, RI, 1996. MR 97c:22001
  • 21. V. Varadarajan, Lie groups, Lie algebras and their representations, Springer-Verlag, New York, 1984. MR 85e:22001

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A65, 43A46, 22E46

Retrieve articles in all journals with MSC (2000): 43A65, 43A46, 22E46

Additional Information

David Grow
Affiliation: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409

Kathryn E. Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Keywords: Characters, independence, compact non-abelian groups, compact Lie groups
Received by editor(s): August 22, 2003
Published electronically: May 20, 2004
Additional Notes: This research was supported in part by NSERC and the Swedish Natural Sciences Research Council
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society