Details:
Title  Computing with real Lie algebras: Real forms, Cartan decompositions, and Cartan subalgebras  Author(s)  Willem A., Heiko Dietrich, Paolo Faccin  Type  Article in Journal  Abstract  Abstract We describe algorithms for performing various tasks related to real simple Lie algebras. These algorithms form the basis of our software package CoReLG, written in the language of the computer algebra system GAP4. First, we describe how to efficiently construct real simple Lie algebras up to isomorphism. Second, we consider a real semisimple Lie algebra g . We provide an algorithm for constructing a maximally (non)compact Cartan subalgebra of g ; this is based on the theory of Cayley transforms. We also describe the construction of a Cartan decomposition g = k ⊕ p . Using these results, we provide an algorithm to construct all Cartan subalgebras of g up to conjugacy; this is a constructive version of a classification theorem due to Sugiura.  Keywords  Real simple Lie algebras, Cartan decompositions, Cartan subalgebras  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717113000709 
Language  English  Journal  Journal of Symbolic Computation  Volume  56  Number  0  Pages  27  45  Year  2013  Edition  0  Translation 
No  Refereed 
No 
