Main Article Content
Abstract
Keywords
Article Details
References
- Koca, M. and Koc, R. Octonions and the Group of Order 1344. Turkish Journal of Physics, 1995, 19, 304-319.
- Luhn, C., Nasri, S. and Ramond, P. Simple finite non-Abelian flavor groups. Journal of MathematicalPhysics, 2007, 48(12), 123519.
- Luhn, C., Nasri, S. and Ramond, P. Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 xZ_3. Physics Letters B, 2007, 652(1), 27-33.
- Pakvasa S., and Sugawara, H. Discrete symmetry and Cabibbo angle. Physics Letters B, 1978, 73, 61-64;Grimus, W. and Lavoura, L. S3 x Z2 model for neutrino mass matrices. Journal of High Energy Physics(JHEP), 2005, 08:013; Grimus, W. and Lavoura, L. A model realizing the Harrison-Perkins-Scott lepton mixing matrix. Journal of High Energy Physics, 2006, 01:018; Mohapatra, R.N., Nasri, S. and Yu, H.B. S3
- symmetry and tri-bimaximal mixing. Physics Letters B, 2006, 639(3-4), 318-321.
- Babu, K.S., Ma, E. and Valle, J.W.F. Underlying A4 symmetry for the neutrino mass matrix and the quark mixing matrix. Physics Letters B, 2003, 552, 207-213.
- Hagedorn, C., Lindner, M. and Mohapatra, R.N. S4 flavor symmetry of quarks and leptons in SU(5) Grand Unified Theory. Journal of High Energy Physics, 2006, 06:042.
- Varzielas, I. de Medeiros and Ross, G.G. SU(3) family symmetry and neutrino bi-tri-maximal mixing. Nuclear Physics B, 2006, 733(1), 31-47.
- Kaplan, D.B. and Schmaltz, M. Flavor unification and discrete non-Abelian symmetries. Physics Review D, 1994, 49 (7), 3741-3750.
- Ma, E. Near Tribimaximal neutrino mixing with delta (27) symmetry. Physics Letters B, 2008, 660, 505-507.
- Harrison, P.F., Perkins, D.H. and Scott, W.G. Tri-bimaximal mixing and the neutrino oscillation data. Physics Letters B, 2002, 530, 167-173.
- Conway, J.H, Curtis, R.T., Norton, S.P , Parker, R.A. and Wilson, R.A., Atlas of Finite Groups. Oxford University Presss, 1985.
- Bauer, M. and Itzykson, C. Modular transformations of SU(N) affine characters and their commutant. Communications in Mathematical Physics, 1990, 127(3), 617-636.
- King, R.C., Toumazet, F. and Wybourne, B.G. A finite subgroup of the exceptional Lie group G2. Journal of Physics A: Mathematical and General, 1999, 32(48), 8527-8537.
- Gunaydin, M. and Gursey, F. Quark structure and octonions. Journal of Mathematical Physics, 1973, 14 (11), 1651-1667.
- Karsch, F. and Koca, M. G2 as the Automorphism Group of Octonionic Root System of E7. Journal of Physics A: Mathematical and General, 1990, 23(21), 4739-4750; Koca, M., Koc, R. and Koca, N.O. The chevalley group G2 of order 12096 and the octonionic root system of E7. Linear Algebra and its Applications,
- , 422, 808-823.
- Coxeter, H.S.M. and Moser, W.O.J. Generators and Relations for Discrete Groups. Springer Verlag, 1965; H.S.M. Coxeter, Regular Complex Polytopes. Cambridge University Press, 1973.
- Conway, J.H. and Smith, D.A. On Quaternion’s and Octonions: Their Geometry, Arithmetics and Symmetry. A.K. Peters, Ltd, Natick, MA, 2003.
- Koca, M., Koc, R. and Al-Barwani, M. Quaternionic Roots of SO(8), SO(9), F4 and the Related Weyl Groups. Journal of Mathematical Physics, 2003, 44, 3123-3140; Koca, M., Koc, R. and Al-Barwani, M. Quaternionic root systems and subgroups of the Aut (F4). Journal of Mathematical Physics, 2006, 47, 043507- 043521.
- Conway, J.H. Three Lectures on Exceptional Groups, Chap 10 in Conway, J.H. and Sloane, N.J.A. Sphere Packings, Lattices and Groups, Springer Verlag, 1998.
References
Koca, M. and Koc, R. Octonions and the Group of Order 1344. Turkish Journal of Physics, 1995, 19, 304-319.
Luhn, C., Nasri, S. and Ramond, P. Simple finite non-Abelian flavor groups. Journal of MathematicalPhysics, 2007, 48(12), 123519.
Luhn, C., Nasri, S. and Ramond, P. Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 xZ_3. Physics Letters B, 2007, 652(1), 27-33.
Pakvasa S., and Sugawara, H. Discrete symmetry and Cabibbo angle. Physics Letters B, 1978, 73, 61-64;Grimus, W. and Lavoura, L. S3 x Z2 model for neutrino mass matrices. Journal of High Energy Physics(JHEP), 2005, 08:013; Grimus, W. and Lavoura, L. A model realizing the Harrison-Perkins-Scott lepton mixing matrix. Journal of High Energy Physics, 2006, 01:018; Mohapatra, R.N., Nasri, S. and Yu, H.B. S3
symmetry and tri-bimaximal mixing. Physics Letters B, 2006, 639(3-4), 318-321.
Babu, K.S., Ma, E. and Valle, J.W.F. Underlying A4 symmetry for the neutrino mass matrix and the quark mixing matrix. Physics Letters B, 2003, 552, 207-213.
Hagedorn, C., Lindner, M. and Mohapatra, R.N. S4 flavor symmetry of quarks and leptons in SU(5) Grand Unified Theory. Journal of High Energy Physics, 2006, 06:042.
Varzielas, I. de Medeiros and Ross, G.G. SU(3) family symmetry and neutrino bi-tri-maximal mixing. Nuclear Physics B, 2006, 733(1), 31-47.
Kaplan, D.B. and Schmaltz, M. Flavor unification and discrete non-Abelian symmetries. Physics Review D, 1994, 49 (7), 3741-3750.
Ma, E. Near Tribimaximal neutrino mixing with delta (27) symmetry. Physics Letters B, 2008, 660, 505-507.
Harrison, P.F., Perkins, D.H. and Scott, W.G. Tri-bimaximal mixing and the neutrino oscillation data. Physics Letters B, 2002, 530, 167-173.
Conway, J.H, Curtis, R.T., Norton, S.P , Parker, R.A. and Wilson, R.A., Atlas of Finite Groups. Oxford University Presss, 1985.
Bauer, M. and Itzykson, C. Modular transformations of SU(N) affine characters and their commutant. Communications in Mathematical Physics, 1990, 127(3), 617-636.
King, R.C., Toumazet, F. and Wybourne, B.G. A finite subgroup of the exceptional Lie group G2. Journal of Physics A: Mathematical and General, 1999, 32(48), 8527-8537.
Gunaydin, M. and Gursey, F. Quark structure and octonions. Journal of Mathematical Physics, 1973, 14 (11), 1651-1667.
Karsch, F. and Koca, M. G2 as the Automorphism Group of Octonionic Root System of E7. Journal of Physics A: Mathematical and General, 1990, 23(21), 4739-4750; Koca, M., Koc, R. and Koca, N.O. The chevalley group G2 of order 12096 and the octonionic root system of E7. Linear Algebra and its Applications,
, 422, 808-823.
Coxeter, H.S.M. and Moser, W.O.J. Generators and Relations for Discrete Groups. Springer Verlag, 1965; H.S.M. Coxeter, Regular Complex Polytopes. Cambridge University Press, 1973.
Conway, J.H. and Smith, D.A. On Quaternion’s and Octonions: Their Geometry, Arithmetics and Symmetry. A.K. Peters, Ltd, Natick, MA, 2003.
Koca, M., Koc, R. and Al-Barwani, M. Quaternionic Roots of SO(8), SO(9), F4 and the Related Weyl Groups. Journal of Mathematical Physics, 2003, 44, 3123-3140; Koca, M., Koc, R. and Al-Barwani, M. Quaternionic root systems and subgroups of the Aut (F4). Journal of Mathematical Physics, 2006, 47, 043507- 043521.
Conway, J.H. Three Lectures on Exceptional Groups, Chap 10 in Conway, J.H. and Sloane, N.J.A. Sphere Packings, Lattices and Groups, Springer Verlag, 1998.