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|Title:||Extending π-systems to bases of root systems||Authors:||Aslaksen, H.
|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|
|Appears in Collections:||Staff Publications|
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