2012/12/13 by Aaron Wangberg, Wangberg, Aaron, Tevian Dray +1
Mathematics · #17A35 #17B81 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:17A35 #msc:17B81
paper · pdf · doi:10.48550/arxiv.1212.3182
18 pages, 3 tables, 6 figures
arxiv created 2012/12/13 · openalex publication_date 2012/12/13 · arxiv updated 2012/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the subalgebra structure of sl(3,O), a particular real form of e6 chosen for its relevance to particle physics and its close relation to generalized Lorentz groups. We use an explicit representation of the Lie group SL(3,O) to construct the multiplication table of the corresponding Lie algebra sl(3,O). Both the multiplication table and the group are then utilized to find various nested chains of subalgebras of sl(3,O), in which the corresponding Cartan subalgebras are also nested where possible. Because our construction involves the Lie group, we simultaneously obtain an explicit representation of the corresponding nested chains of subgroups of SL(3,O).