A possible framework of the Lipkin model obeying the SU (n) algebra in arbitrary fermion number. I: The SU (2) algebras extended from the conventional fermion pair and determination of the minimum weight states Yasuhiko Tsue1,2,∗, Constanca Providencia, Joao da Providencia, and MasatoshiYamamura 1CFisUC, Departamento de Fisica, Universidade de Coimbra, 3004-516 Coimbra, Portugal 2Physics Division, Faculty of Science, Kochi University, Kochi 780-8520, Japan 3Department of Pure andApplied Physics, Faculty of Engineering Science, Kansai University, Suita 564-8680, Japan ∗E-mail: tsue@kochi-u.ac.jp