Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CONJUGACY CLASSIFICATION OF n-DIMENSIONAL MÖBIUS GROUP

  • Binlin Dai (School of Mathematics Shanghai University of Finance and Economics) ;
  • Zekun Li (School of Mathematics Shanghai University of Finance and Economics)
  • Received : 2021.12.26
  • Accepted : 2022.12.30
  • Published : 2023.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the n-dimensional Möbius transformation. We obtain several conjugacy invariants and give a conjugacy classification for n-dimensional Möbius transformation.

Keywords

Acknowledgement

The authors heartily thank the referee for a careful reading of this paper as well as for many useful comments and suggestions.

References

  1. 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
  2. L. V. Ahlfors, H. E. Rauch, function theorist, in Differential geometry and complex analysis, 15-31, Springer, Berlin, 1985.
  3. 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
  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
  5. 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.
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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.