2008/02/19 by V. M. Red’kov, Victor M. Red'kov, Andrei A. Bogush +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Finite Group Theory Research #graph theory and CDMA systems #math-ph #math.MP
paper · pdf · doi:10.3842/sigma.2008.021
published as SIGMA 4 (2008), 021, 46 pages · This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
arxiv created 2008/02/19 · openalex publication_date 2008/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Parametrization of 4 4-matrices G of the complex linear group GL(4, C) in terms of four complex 4-vector parameters (k, m, n, l) is investigated. Additional restrictions separating some subgroups of GL(4, C) are given explicitly. In the given parametrization, the problem of inverting any 44 matrix G is solved. Expression for determinant of any matrix G is found: det G = F (k, m, n, l). Unitarity conditions G + = G -1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G 1 , G 2 , G 3 -each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU (2) and 1parametric Abelian group. The Dirac basis of generators k , being of Gell-Mann type, substantially differs from the basis i used in the literature on SU (4) group, formulas relating them are found -they permit to separate SU (3) subgroup in SU (4). Special way to list 15 Dirac generators of GL(4, C) can be used