2017/01/31 by D. Jurciukonis, Darius Jurčiukonis, L. Lavoura +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Cryptography and Residue Arithmetic #Extant taxon #Finite Group Theory Research #Geometric and Algebraic Topology #Group (periodic table) #Irreducible representation #Listing (finance) #Order (exchange) #Product (mathematics) #Representation (politics) #Series (stratigraphy) #hep-ph #math-ph #math.MP #math.RT
paper · pdf · doi:10.1093/ptep/ptx064
published as Prog. Theor. Exp. Phys. 2017, 053A03 · 54 pages, no figures
arxiv created 2017/01/31 · openalex created_date 2017/02/17 · openalex publication_date 2017/04/24 · arxiv updated 2017/05/30 · openalex updated_date 2026/08/05
We have sorted the SmallGroups library of all the finite groups of order smaller than 2000 to identify the groups that possess a faithful three-dimensional irreducible representation (`irrep') and cannot be written as the direct product of a smaller group times a cyclic group. Using the computer algebra system GAP, we have scanned all the three-dimensional irreps of each of those groups to identify those that are subgroups of SU(3); we have labelled each of those subgroups of SU(3) by using the extant complete classification of the finite subgroups of SU(3). Turning to the subgroups of U(3) that are not subgroups of SU(3), we have found the generators of all of them and classified most of them in series according to their generators and structure.