Original Articles

The generalized Borel-de Siebenthal theorem

Published in: Quaestiones Mathematicae
Volume 38 , issue 4 , 2015 , pages: 529–534

DOI: 10.2989/16073606.2014.981732

Author(s): Ching-I Hsin Department of Computer Science and Information Engineering, Hsinchu County, Taiwan

Keywords: 05C22 , 05C25 , 17B20 , 17B22 , 05C22 , 05C25 , 17B20 , 17B22

Abstract

Let D be a Dynkin diagram. The classical Borel-de Siebenthal theorem uses an algorithm to simplify every painting on D to one with a single black vertex. In ^{this article, we generalize this theorem to elements of Z}n^{, so that n=2 corresponds}to the paintings. We also explain the algebraic significance of this result in terms of automorphisms on complex simple Lie algebras.

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