Schottky groups cannot act on ℙ²ⁿ_ℂ as subgroups of PSL(2n+1,ℂ)

2008/06/10 by Angel Cano, Cano, Angel
Computer Science · Engineering · Mathematics · #37F99 #Advanced Graph Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.DS #msc:37F99

paper · pdf · doi:10.48550/arxiv.0806.1705

9 pages. To appear in Bulletin of the Brazilian Mathematical Society. The original publication is available at http://www.springerlink.com

arxiv created 2008/06/10 · openalex publication_date 2008/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we look at a special type of discrete subgroups of PSL_n+1(ℂ) called Schottky groups. We develop some basic properties of these groups and their limit set when n > 1, and we prove that Schottky groups only occur in odd dimensions, \it i.e., they cannot be realized as subgroups of PSL_2n+1(ℂ).

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