Extensions of Pontryagin hypergroups

• Autorzy: Heyer H. , Kawakami S.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to investigate the extension problem for the category of commutative hypergroups. In fact, by applying the new notion of a field of compact subhypergroups, sufficiently many extensions can be established, and among them splitting extensions can be characterized. Moreover, the duality of extensions will be studied via duality of fields of hypergroups. The method of extension via fields of hypergroups yields the construction of Pontryagin hypergroups which do not arise from group-theoretic objects.

Słowa kluczowe

EN

hypergroups; extensions; duality

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 2
• Strony: 245--260
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Heyer H.

• Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, 72076, Tübingen, Germany

autor

Kawakami S.

• Nara University of Education, Department of Mathematics, Takabatake-cho, Nara, 630-8528, Japan

Bibliografia

• [1] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Stud. Math. 20 (1995).
• [2] C. F. Dunkl and D. E. Ramirez, A family of compact P*-hypergroups, Trans. Amer. Math. Soc. 202 (1975), pp. 339-356.
• [3] J. J. F. Fournier and K. A. Ross, Random Fourier series on compact abelian hypergroups, J. Aust. Math. Soc. Ser. A 37 (1) (1984), pp. 45-81.
• [4] P. Hermann and M. Voit, Induced representation and duality results for commutative hypergroups, Forum Math. 7 (1995), pp. 543-558.
• [5] H. Heyer, T. Jimbo, S. Kawakami and K. Kawasaki, Finite commutative hypergroups associated with actions of finite abelian groups, Bull. Nara Univ. Ed. 54 (2) (2005), pp. 23-29.
• [6] H. Heyer, Y. Katayama, S. Kawakami and K. Kawasaki Extensions of finite commutative hypergroups, preprint.
• [7] R. I. Jewett, Spaces with an abstract convolution of measures, Adv. Math. 18 (1) (1975), pp. 1-101.
• [8] S. Kawakami and W. Ito, Crossed products of commutative finite hypergroups, Bull. Nara Univ. Ed. 48 (2) (1999), pp. 1-6.
• [9] K. A. Ross, Centers of hypergroups, Trans. Amer. Math. Soc. 243 (1978), pp. 251-269.
• [10] K. Urbanik, Generalized convolutions, Studia Math. 23 (1964), pp. 217-245.
• [11] M. Voit, Projective and inductive limits of hypergroups, Proc. London Math. Soc. 67 (1993), pp. 617-648.
• [12] M. Voit, Substitution of open subhypergroups, Hokkaido Math. J. 23 (1994), pp. 143-183.
• [13] R. C. Vrem, Connectivity and supernormality results for hypergroups, Math. Z. 195 (3) (1987), pp. 419-428.
• [14] R. C. Vrem, Hypergroup joins and their dual objects, Pacific J. Math. 111 (2) (1989), pp. 483-495.
• [15] N. J. Wildberger, Finite commutative hypergroups and applications from group theory to conformal field theory, in: Applications of Hypergroups and Related Measure Algebras, Amer. Math. Soc., Providence 1994, pp. 413-434.
• [16] Hm. Zeūner, Duality of commutative hypergroups, in: Probability Measures on Groups, X. H. Heyer (Ed.), Plenum Press, New York-London 1991, pp. 467-488.

Uwagi

To the memory of Professor Kazimierz Urbanik.