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http://dx.doi.org/10.4134/CKMS.2016.31.1.177

ON THE CONJUGACY OF MÖBIUS GROUPS IN INFINITE DIMENSION  

Fu, Xi (Department of Mathematics Shaoxing University)
Lu, Bowen (Department of Mathematics Shaoxing University, School of International Business Zhejiang International Studies University)
Publication Information
Communications of the Korean Mathematical Society / v.31, no.1, 2016 , pp. 177-184 More about this Journal
Abstract
In this paper, we establish some conjugacy criteria of $M\ddot{o}bius$ groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.
Keywords
trace; hyperbolic; conjugate;
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1 L. V. Ahlfors, On the fixed points of Mobius transformations in ${\bar{\mathbb{R}}{^n}$, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 15-27.   DOI
2 B. N. Apanasov, The Geometry of Discrete Groups and Manifolds, Nauka, Moscow, 1991.
3 M. Chen, The extension of Mobius groups, Complex Var. Theory Appl. 47 (2002), no. 3, 225-228.   DOI
4 M. Frunza, Mobius transformations in infinite dimension, Rev. Roumaine Math. Pures Appl. 36 (1991), no. 7-8, 369-376.
5 X. Fu and B. Xie, A characterization of Fuchsian groups in SU(n, 1), Complex Var. Elliptic Equ. 59 (2014), no. 5, 723-731.   DOI
6 J. Kim, Quaternionic hyperbolic Fuchsian groups, Linear Algebra Appl. 438 (2013), no. 9, 3610-3617.   DOI
7 L. Li, Ball-preserving Mobius transformations in infinite dimension, Complex Var. Elliptic Equ. 54 (2009), no. 7, 697-703.   DOI
8 L. Li, A generalization of Jorgensen's inequality to infinite dimension, New York J. Math. 17 (2011), 41-49.
9 L. Li, An inequality on parabolic Mobius groups in infinite dimension and its application, Acta Math. Sci. Ser. A Chin. Ed. 32 (2012), no. 2, 349-355.
10 L. Li, Discreteness of Mobius groups in infinite dimension, Complex Var. Elliptic Equ. 58 (2013), no. 1, 109-112.   DOI
11 B. Maskit, Kleinian Groups, Springer-Verlag, New York, 1987.
12 X. Wang and W. Yang, Generating systems of subgroups in PSL(2, ${\Gamma}_n$), Proc. Edinb. Math. Soc. (2) 45 (2002), no. 1, 49-58.   DOI
13 P. Waterman, Mobius transformations in several dimensions, Adv. Math. 101 (1993), no. 1, 87-113.   DOI