Abstract
This paper introduces the parastatistics induced by algebras. It accommodates four kinds of particles: ordinary bosons and three types of parabosons which mutually anticommute when belonging to different type (so far, in the literature, only parastatistics induced by superalgebras and producing parafermions have been considered). It is shown how to detect parabosons in the multi-particle sector of a quantum model. The difference with respect to a system composed by ordinary bosons is spotted by measuring some selected observables on certain given eigenstates. The construction of the multi-particle states is made through the appropriate braided tensor product. The application of - and -gradings produces 9 inequivalent multi-particle Hilbert spaces of a 4 × 4 matrix oscillator. The parabosonic Hilbert space is one of them.
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