An Algorithm for Computing Ideals and Conjugacy Classes of Subalgebras of Borel Subalgebras

Abstract

In this article, we present a constructive procedure for determining all ideals of the Borel subalgebra of a complex semisimple Lie algebra from its root system or, equivalently, its Dynkin diagram. The proposed algorithmic approach has been implemented in Maple. The Maple code has been tested on Borel subalgebras associated with both classical and exceptional Lie algebras. An interactive procedure is also given to determine conjugacy classes of all subalgebras in the derived algebra of the Borel subalgebra.