Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T13:43:13.106Z Has data issue: false hasContentIssue false
  • English
  • Français

DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  10 June 2016

MAHMOOD ALAGHMANDAN  and
MASSOUD AMINI
MAHMOOD ALAGHMANDAN
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg SE-412 96, Sweden e-mail: [email protected]
MASSOUD AMINI
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

MSC classification

Primary: 43A62: Hypergroups
Secondary: 43A40: Character groups and dual objects 43A65: Representations of groups, semigroups, etc.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 421 - 435
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

REFERENCES

1. Alaghmandan, M., Approximate amenability of Segal algebras, J. Aust. Math. Soc. 95 (1) (2013), 20–35.Google Scholar
2. Alaghmandan, M., Choi, Y. and Samei, E., ZL-amenability constants of finite groups with two character degrees, Canad. Math. Bull. 57 (3) (2014), 449–462.Google Scholar
3. Alaghmandan, M. and Spronk, N., Amenability properties of the central Fourier algebra of a compact group, (to appear).Google Scholar
4. Amini, M. and Medghalchi, A. R., Amenability of compact hypergroup algebras, Math. Nachr. 287 (14–15) (2014), 1609–1617.CrossRefGoogle Scholar
5. Azimifard, A., Samei, E. and Spronk, N., Amenability properties of the centres of group algebras, J. Funct. Anal. 256 (5) (2009), 1544–1564.Google Scholar
6. Bloom, W. R. and Heyer, H., Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, vol. 20 (Walter de Gruyter & Co., Berlin, 1995).Google Scholar
7. Choi, Y., A gap theorem for the zl-amenability constant of a finite group, Int. J. Group Theory, 5 (4) (2016), 27–46.Google Scholar
8. Chua, K. S. and Ng, W. S., A simple proof of the uncertainty principle for compact groups, Expo. Math. 23 (2) (2005), 147–150.Google Scholar
9. Daher, R. and Kawazoe, T., An uncertainty principle on Sturm-Liouville hypergroups, Proc. Japan Acad. Ser. A Math. Sci. 83 (9–10) (2007), 167–169.CrossRefGoogle Scholar
10. Folland, G. B., A course in abstract harmonic analysis, Studies in Advanced Mathematics (CRC Press, Boca Raton, FL, 1995).Google Scholar
11. Ghandehari, M., Hatami, H. and Spronk, N., Amenability constants for semilattice algebras, Semigroup Forum 79 (2) (2009), 279–297.Google Scholar
12. Hartmann, K., Wim Henrichs, R. and Lasser, R., Duals of orbit spaces in groups with relatively compact inner automorphism groups are hypergroups, Monatsh. Math. 88 (3) (1979), 229–238.Google Scholar
13. Hewitt, E. and Ross, K. A., Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band, vol. 152 (Springer-Verlag, New York, 1970).Google Scholar
14. Jewett, R. I., Spaces with an abstract convolution of measures, Adv. Math. 18 (1) (1975), 1–101.Google Scholar
15. Johnson, B. E., Non-amenability of the Fourier algebra of a compact group, J. London Math. Soc. (2) 50 (2) (1994), 361–374.Google Scholar
16. Kumar, A., A qualitative uncertainty principle for hypergroups, in Functional analysis and operator theory (New Delhi, 1990), Lecture Notes in Math., vol. 1511 (Springer, Berlin, 1992), 1–9.Google Scholar
17. Mosak, R. D., The L 1- and C*-algebras of [FIA]- B groups, and their representations, Trans. Amer. Math. Soc. 163 (1972), 277–310.Google Scholar
18. Rösler, M. and Voit, M., An uncertainty principle for ultraspherical expansions, J. Math. Anal. Appl. 209 (2) (1997), 624–634.Google Scholar
19. Ross, K. A., Centers of hypergroups, Trans. Amer. Math. Soc. 243 (1978), 251–269.Google Scholar
20. Saeki, S., On norms of idempotent measures, Proc. Amer. Math. Soc. 19 (1968), 600–602.Google Scholar
21. Stokke, R., Approximate diagonals and Følner conditions for amenable group and semigroup algebras, Studia Math. 164 (2) (2004), 139–159.Google Scholar
22. Voit, M., An uncertainty principle for commutative hypergroups and Gel'fand pairs, Math. Nachr. 164 (1993), 187–195.Google Scholar
23. Vrem, R. C., Harmonic analysis on compact hypergroups, Pacific J. Math. 85 (1) (1979), 239–251.Google Scholar
24. Vrem, R. C., Hypergroup joins and their dual objects, Pacific J. Math. 111 (2) (1984), 483–495.CrossRefGoogle Scholar
25. Wildberger, N. J., Finite commutative hypergroups and applications from group theory to conformal field theory, in Applications of hypergroups and related measure algebras (Seattle, WA, 1993), Contemp. Math., vol. 183 (Amer. Math. Soc., Providence, RI, 1995), 413–434.Google Scholar