Abstract
Equivalence between algebraic structures generated by parastatistics triple relations of Green (1953) and Greenberg-Messiah (1965), and certain orthosymplectic ℤ2 × ℤ2-graded Lie superalgebras is found explicitly. Moreover, it is shown that such superalgebras give more complex para-Fermi and para-Bose systems then ones of Green-Greenberg-Messiah.
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