2007/08/06 by Roldao da Rocha, R. da Rocha, Jayme Vaz Jr +1 · 1 citation
Mathematics · Physics and Astronomy · Social Sciences · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #International Science and Diplomacy #hep-th #math-ph #math.MP #msc:15A66 #msc:32G81 #msc:81R05
paper · pdf · doi:10.1007/s10773-007-9362-x
published as Int.J.Theor.Phys.46:2464-2487,2007 · 19 pages
openalex publication_date 2007/08/06 · arxiv created 2007/10/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.