Paraboson quotients. A braided look at Green ansatz and a generalization

Abstract

Bosons and Parabosons are described as associative superalgebras, with an infinite number of odd generators. Bosons are shown to be a quotient superalgebra of Parabosons, establishing thus an even algebra epimorphism which is an immediate link between their simple modules. Parabosons are shown to be a super-Hopf algebra. The super-Hopf algebraic structure of Parabosons, combined with the projection epimorphism previously stated, provides us with a braided interpretation of the Green's ansatz device and of the parabosonic Fock-like representations. This braided interpretation combined with an old problem leads to the construction of a straightforward generalization of Green's ansatz.