CoReLG swMATH ID: 8646 Software Authors: Dietrich, Heiko; Faccin, Paolo; de Graaf, Willem A. Description: Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras. 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. Homepage: http://www.gap-system.org/Packages/corelg.html Keywords: real simple Lie algebras; Cartan decomposition; Cartan subalgebras Related Software: GAP; SLA; Magma; NoCK; CKForms; LiE; MathOverflow; SageMath; Sophus; HNC; LiePRing; FPLSA; QuaGroup; LieAlgDB; LieRing Cited in: 14 Documents all top 5 Cited by 17 Authors 8 de Graaf, Willem Adriaan 4 Dietrich, Heiko 4 Faccin, Paolo 2 Ali, Sajid 2 Azad, Hassan 2 Biswas, Indranil 2 Bocheński, Maciej Franciszek 2 Jastrzębski, Piotr 2 Tralle, Aleksy E. 1 Bächle, Andreas 1 Borovoi, Mikhail V. 1 Ghanam, Ryad A. 1 Letzter, Gail 1 Levasseur, Thierry 1 Mustafa, Muhammad Tahir 1 Sambale, Benjamin 1 Stafford, J. Toby all top 5 Cited in 7 Serials 5 Journal of Symbolic Computation 1 Mathematics of Computation 1 Compositio Mathematica 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Monatshefte für Mathematik 1 Representation Theory all top 5 Cited in 11 Fields 12 Nonassociative rings and algebras (17-XX) 5 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Computer science (68-XX) 2 Number theory (11-XX) 2 Associative rings and algebras (16-XX) 1 Partial differential equations (35-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year