On the Discreteness and Convergence in n-Dimensional Mobius Groups |
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Authors: | Ainong, Fang Bing, Nai |
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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 algebraCn1, the Clifford matrix group SL(2, n), the Cliffordnorm of ||A||=(|a|2+|b|2+|c|2+|d|2) (1) and the Clifford metric of SL(2, n) or of the Möbius groupM(Rn) d(A1,A2)=||A1A2||(|a1a2|2+|b1b2|2+|c1c2|2+|d1d2|2)(2) where |·| is the norm of a Clifford number and represents fi M(), i = 1,2, and so on. In addition, we adopt some notions in [6, 12]:the elementary group, the uniformly bounded torsion, and soon. For example, the definition of the uniformly bounded torsionis as follows. |
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