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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commuting isometries of the complex hyperbolic space


Authors: Wensheng Cao and Krishnendu Gongopadhyay
Journal: Proc. Amer. Math. Soc. 139 (2011), 3317-3326
MSC (2010): Primary 51M10; Secondary 51F25, 20G20
Published electronically: February 11, 2011
MathSciNet review: 2811286
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Abstract: Let $ H_{\mathbb{C}}^n$ denote the complex hyperbolic space of dimension $ n$. The group $ U(n,1)$ acts as the group of isometries of $ H_{\mathbb{C}}^n$. In this paper we investigate when two isometries of the complex hyperbolic space commute. Along the way we determine the centralizers.


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Additional Information

Wensheng Cao
Affiliation: School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong 529020, People’s Republic of China
Email: wenscao@yahoo.com.cn

Krishnendu Gongopadhyay
Affiliation: Indian Institute of Science Education and Research (IISER) Mohali, Transit Campus: MGSIPAP Complex, Sector-26, Chandigarh 160019, India
Email: krishnendu@iisermohali.ac.in, krishnendug@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10796-2
PII: S 0002-9939(2011)10796-2
Keywords: Complex hyperbolic space, isometries, centralizers
Received by editor(s): January 26, 2010
Received by editor(s) in revised form: January 27, 2010, and August 21, 2010
Published electronically: February 11, 2011
Additional Notes: The first author was supported by the NSF of China (No. 10801107) and the NSF of Guangdong Province (No. 8452902001000043)
Communicated by: Michael Wolf
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.