Contraction groups and scales of automorphisms of totally disconnected locally compact groups

Israel Journal of Mathematics

Volumn 142, Issue , 2004, Pages 221-248

  Baumgartner, Udo ^a   Willis, George A ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 6344293781     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02771534     Document Type: Article

References (26)

1. [Bou68] N. Bourbaki, Groupes et Algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris, 1968; publiées dans Actualités scientifiques et industriels 1337.
2. [BT65] A. Borel and J. Tits, Groupes réductifs, Publications mathématiques de l'Institut des Hautes Études Scientifiques 27 (1965), 55-150.
3. [DD89] W. Dicks and M. J. Dunwoody, Groups acting on Graphs, Volume 17 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1989.
4. [DS91] S. G. Dani and R. Shah, Contraction subgroups and semistable measures on p-adic Lie groups, Mathematical Proceedings of the Cambridge Philosophical Society 110 (1991), 299-306.
5. [Glö98a] H. Glöckner, Scale functions on linear groups over local skew fields, Journal of Algebra 205 (1998), 525-541.
6. [Glö98b] H. Glöckner, Scale functions on p-adic Lie groups, Manuscripta Mathematica 97 (1998), 205-215.
7. [GW02] H. Glöckner and G. A. Willis, Topologization of Hecke pairs and Hecke C*-algebras, Topology Proceedings 26 (2001-2002), 565-591.
8. [Haz88] M. Hazewinkel (ed.), Encyclopaedia of Mathematics. Vol. 1. A-B, D. Reidel Publ. Co., Dordrecht, 1988. Translated from the Russian.
9. [HR79] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis; Volume I, Volume 115 of Grundlehren der mathematischen Wissenschaften, second edition, Springer-Verlag, Berlin, 1979.
10. [HS88] W. Hazod and E. Siebert, Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups, Journal of Theoretical Probability 1 (1988), 211-225.
11. [LR68] H. Leptin and L. Robertson, Every locally compact MAP group is unimodular, Proceedings of the American Mathematical Society 19 (1968), 1079-1082.
12. [Mar89] G. A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Volume 17 (3. Folge) of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, New York, 1989.
13. [Möl02] R. G. Möller, Structure theory of totally disconnected locally compact groups via graphs and permutations, Canadian Journal of Mathematics 54 (2002), 795-827.
14. [Moo80] C. C. Moore, The Mautner phenomenon for general unitary representations, Pacific Journal of Mathematics 86 (1980), 155-169.
15. [MR76] P. R. Müller-Römer, Kontrahierende Erweiterungen und kontrahierbare Gruppen, Journal für die reine und angewandte Mathematik 283/284 (1976), 238-264.
16. [Pra82] G. Prasad, Elementary proof of a theorem of Bruhat-Tits-Rousseau and of a theorem of Tits, Bulletin de la Société Mathématique de France 110 (1982), 197-202.
17. [RD81] W. Roelcke and S. Dierolf, Uniform Structures on Topological Groups and their Quotients, McGraw-Hill International Book Company, New York, 1981.
18. [Ros79] J. Rosenblatt, A distal property of groups and the growth of connected locally compact groups, Mathematika 26 (1979), 94-98.
19. 2 was published as Astérisque 46 (by Société Mathématique de France) in 1977.
20. 2 was published as Astérisque 46 (by Société Mathématique de France) in 1977.
21. [Sie86] E. Siebert, Contractive automorphisms on locally compact groups, Mathematische Zeitschrift 191 (1986), 73-90.
22. [Sie89] E. Siebert, Semistable convolution semigroups and the topology of contraction groups, in Probability Measures on Groups IX (Proceedings of a Conference held at Oberwolfach/FRG 1988), Lecture Notes in Mathematics 1379, Springer-Verlag, Berlin, 1989, pp. 325-343.
23. [Wan84] J. S. P. Wang, The Mautner phenomenon for p-adic Lie groups, Mathematische Zeitschrift 185 (1984), 403-412.
24. [Wil] G. A. Willis, Tidy subgroups for commuting automorphisms of totally disconnected locally compact groups: An analogue of simultaneous triangularisation of matrices, New York Journal of Mathematics 10 (2004), 1-35. Available at http://nyjm.albany.edu:8000/j/2004/Vol10.htm.
25. [Wil94] G. A. Willis, The structure of totally disconnected locally compact groups, Mathematische Annalen 300 (1994), 341-363.
26. [Wil01] G. A. Willis, Further properties of the scale function on a totally disconnected locally compact group, Journal of Algebra 237 (2001), 142-164.