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ON THE DISCRETENESS AND CONVERGENCE IN n-DIMENSIONAL MÖBIUS GROUPS

Published online by Cambridge University Press:  01 June 2000

FANG AINONG  and
NAI BING
FANG AINONG
Affiliation:
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China
NAI BING
Affiliation:
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China
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Abstract

Throughout this paper, we adopt the same notations as in [1, 6, 8] such as the Möbius group M(ℝn), the Clifford algebra Cn−1, the Clifford matrix group SL(2, Γn), the Clifford norm of

formula here

and the Clifford metric of SL(2, Γn) or of the Möbius group M(ℝn)

formula here

where [mid ]·[mid ] is the norm of a Clifford number and

formula here

represents fi ∈ M(ℝn), i = 1, 2, and so on. In addition, we adopt some notions in [6, 12]: the elementary group, the uniformly bounded torsion, and so on. For example, the definition of the uniformly bounded torsion is as follows.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 761 - 773
Copyright
The London Mathematical Society 2000

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