A Majorana analog to the parafermion algebra is constructed and shown to be isomorphic to so(n). Ansatz realizations of this algebra are constructed and used to establish the properties of particular representations. The construction of specific so(n) representations is discussed for odd and even n, and for even n the procedure is illustrated explicitly in the case of so(4). By contracting the Majorana parafermion algebra, the para-Grassman algebra and its representation theory are obtained.
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R. S. Dunne (1996) studied this question.
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