Abstract
In this paper the usualZ 2 graded Lie algebra is generalized to a new form, which may be calledZ 2,2 graded Lie algebra. It is shown that there exist close connections between theZ 2,2 graded Lie algebra and parastatistics, so theZ 2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems
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