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The Discrete Subgroups and Jфrgensen’s Inequality for SL(m, Cp)

The Discrete Subgroups and Jфrgensen's Inequality for SL(m, Cp)
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摘要 In this paper, we give discreteness criteria of subgroups of the special linear group on Qp or Cp in two and higher dimensions. Jorgensen's inequality gives a necessary condition for a non- elementary group of M6bius transformations to be discrete. We give a version of JCrgensen's inequality for SL(m, Cp). In this paper, we give discreteness criteria of subgroups of the special linear group on Qp or Cp in two and higher dimensions. Jorgensen's inequality gives a necessary condition for a non- elementary group of M6bius transformations to be discrete. We give a version of JCrgensen's inequality for SL(m, Cp).
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第3期417-428,共12页 数学学报(英文版)
基金 Supported by National Natural Science Foundation of China (Grants Nos. 10831004 and 11271047) by Science and Technology Commission of Shanghai Municipality NSF (Grant No. 10ZR1403700)
关键词 Jorgensen's inequality discreteness criteria non-Archimedean space Jorgensen's inequality, discreteness criteria, non-Archimedean space
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参考文献6

  • 1Kato, F.: Non-archimedean orbifolds covered by Mumford curves. J. Algebraic Geom., 14, 1-34 (2005).
  • 2Armitage, J. V., Parker, J. R.: Jcrgensen's inequality for non-Archimedean metric spaces. Geometry and Dynamics of Groups and Spaces, 265, 97-111 (2008).
  • 3J0rgensen, T.: A note on the subgroups of SL(2, C). Quart. J. MaSh., 28(2), 209-211 (1977).
  • 4Alain, M. R.: A Course in p-adic Analysis, Springer-Verlag, New York, 2000.
  • 5Artin, E.: Algebraic Numbers and Algebraic Function, Nelson, 1968.
  • 6Martin, G. J.: On discrete Mobius groups in all dimensions: A generalization of J0rgensen's inequality. AcSa Math., 163, 253-289 (1989).

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