On the Phan system of the Schur cover of SU(4, 32)
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- 作者：Max Horn
- 关键词：Phan theory ; Phan amalgam ; Group amalgams ; Incidence geometry ; Computer algebra ; GAP ; Coset enumeration ; ACE
- 刊名：Designs, Codes and Cryptography
- 出版年：2008
- 出版时间：June, 2008
- 年：2008
- 卷：47
- 期：1-3
- 页码：243-247
- 全文大小：155.6 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Combinatorics
Coding and Information Theory
Data Structures, Cryptology and Information Theory
Data Encryption
Discrete Mathematics in Computer Science
Information, Communication and Circuits - 出版者：Springer Netherlands
- ISSN：1573-7586
文摘
This article is part of the program described in Bennett et al. (in: Ivanov et al. (ed.) Groups, combinatorics, and geometry, 2003) [3]. We study the Phan amalgams and their universal completions that occur for q = 3 in rank n = 3 for the diagram A 3 = D 3, corresponding to SU(4, 32) ≅ Spin −(6, 3). We show that the associated geometries admit universal 9-fold coverings, by showing that the universal completion of the Phan amalgam is the central extension of SU(4, 32) by its Schur multiplier. This information provides the last missing piece of information in the full classification of Phan amalgams and their universal completions for A n and D n .