Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jalgebra.2004.12.016
Title: Extending π-systems to bases of root systems
Authors: Aslaksen, H. 
Lang, M.L. 
Issue Date: 15-May-2005
Citation: Aslaksen, H., Lang, M.L. (2005-05-15). Extending π-systems to bases of root systems. Journal of Algebra 287 (2) : 496-500. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jalgebra.2004.12.016
Abstract: Let R be an indecomposable root system. It is well known that any root is part of a basis B of R. But when can you extend a set, C, of two or more roots to a basis B of R? A π-system is a linearly independent set of roots such that if α and β are in C, then α - β is not a root. We will use results of Dynkin and Bourbaki to show that with two exceptions, A3Bn and A7E8, an indecomposable π-system whose Dynkin diagram is a subdiagram of the Dynkin diagrams of R can always be extended to a basis of R. © 2005 Published by Elsevier Inc.
Source Title: Journal of Algebra
URI: http://scholarbank.nus.edu.sg/handle/10635/103255
ISSN: 00218693
DOI: 10.1016/j.jalgebra.2004.12.016
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