Abstract
The usual theory of the Lie algebras and the Lie groups rs shown to be formally extended to the cases in which the group parameters commute and/or anticommute in the most general manner. It is then proved that the parafermi and parabose algebras for f degrees of freedom correspond to the Lie algebras of SO (2/+ 1) and of a graded version of Sp (2/, R), respectively. Further the trilinear and bilinear commutation relations for a general system comprising parafermi and parabose fields are shown to coincide with the Lie commutation relations of a certain group in the above-mentioned sense. Throughout our argumentation parafermi and parabose fields can formally be treated in an analogous man ner. It is thus concluded that the fermi-bose similarity that is known to hold in the ordi nary field theory persists also in parafielcl theory.
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