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.

33 pages, Corrected a few misprints and typos of the journal version

References in corpus (3)

• Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras
• Interpretation and Extension of the Green's Ansatz for Paraparticles
• Algebraic structure of the Green's ansatz and its q-deformed analogue

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• Volichenko-type metasymmetry of braided Majorana qubits
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• On the detectability of paraparticles beyond bosons and fermions
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• Representations of the Lie Superalgebra $\mathfrak{osp}(1|2n)$ with Polynomial Bases
• Gradings, Braidings, Representations, Paraparticles: some open problems
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Variants of bosonisation in Parabosonic algebra. The Hopf and super-Hopf structures