Title: Computing with real Lie algebras
Speaker: Heiko Dietrich (Monash University)
Abstract: The structure theory of complex semisimple Lie algebras uses many combinatorial objects such as root systems, Weyl groups, and Dynkin diagrams, which makes the theory accessible for computer investigations. Computer algebra systems, like GAP, Magma, and LiE, contain software for computing with complex Lie algebras. Also the real semisimple Lie algebras are classified, and there exists a detailed structure theory. However, with the exception of the ATLAS project (USA), there has not been much effort to develop software for computing with real semisimple Lie algebras. We report on the functionality and the underlying theory of our GAP package 'CoReLG' (Computing with Real Lie Groups); it provides functions to construct real semisimple Lie algebras, to check for isomorphisms, and to compute Cartan decompositions, Cartan subalgebras, and nilpotent orbits.