Acknowledgement
The authors heartily thank the referee for a careful reading of this paper as well as for many useful comments and suggestions.
References
- L. V. Ahlfors, On the fixed points of Mobius transformations in Rn, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27. https://doi.org/10.5186/aasfm.1985.1005
- L. V. Ahlfors, H. E. Rauch, function theorist, in Differential geometry and complex analysis, 15-31, Springer, Berlin, 1985.
- A. F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, 91, Springer-Verlag, New York, 1983. https://doi.org/10.1007/978-1-4612-1146-4
- W. Cao, On the classification of four-dimensional Mobius transformations, Proc. Edinb. Math. Soc. (2) 50 (2007), no. 1, 49-62. https://doi.org/10.1017/S0013091505000398
- C. Cao and P. L. Waterman, Conjugacy invariants of Mobius groups, in Quasiconformal mappings and analysis (Ann Arbor, MI, 1995), 109-139, Springer, New York, 1998.
- A. Fang and B. Nai, On the discreteness and convergence in n-dimensional Mobius groups, J. London Math. Soc. (2) 61 (2000), no. 3, 761-773. https://doi.org/10.1112/S0024610700008784
- B. Foreman, Conjugacy invariants of Sl(2, H), Linear Algebra Appl. 381 (2004), 25-35. https://doi.org/10.1016/j.laa.2003.11.002
- X. Fu and B. Lu, On the conjugacy of Mobius groups in infinite dimension, Commun. Korean Math. Soc. 31 (2016), no. 1, 177-184. https://doi.org/10.4134/CKMS.2016.31.1.177
- K. Gongopadhyay, Algebraic characterization of the isometries of the hyperbolic 5-space, Geom. Dedicata 144 (2010), 157-170. https://doi.org/10.1007/s10711-009-9394-x
- Y. Kim, Geometric classification of isometries acting on hyperbolic 4-space, J. Korean Math. Soc. 54 (2017), no. 1, 303-317. https://doi.org/10.4134/JKMS.j150734
- J. R. Parker and I. Short, Conjugacy classification of quaternionic Mobius transformations, Comput. Methods Funct. Theory 9 (2009), no. 1, 13-25. https://doi.org/10.1007/BF03321711
-
X. Wang, L. Li, and W. Cao, Discreteness criteria for Mobius groups acting on
$\overline{{\mathbb{R}}^n}$ , Israel J. Math. 150 (2005), 357-368. https://doi.org/10.1007/BF02762387 - X. Wang, Algebraic convergence theorems of n-dimensional Kleinian groups, Israel J. Math. 162 (2007), 221-233. https://doi.org/10.1007/s11856-007-0096-5
- Z. Yu, J. Wang, and F. Ren, The conjugate classification and type criteria of Mobius transformations in higher dimensions, J. Fudan Univ. Nat. Sci. 35 (1996), no. 4, 374-380.