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

TL;DR

This paper explores the algebraic structure of parabosons, establishing their relation to bosons, and introduces a braided interpretation of Green's ansatz, leading to a novel generalization of parabosonic representations.

Contribution

It provides a braided algebraic perspective on parabosons and generalizes Green's ansatz using super-Hopf algebra structures.

Findings

Parabosons are shown to be a super-Hopf algebra.

A braided interpretation of Green's ansatz is developed.

A new generalization of Green's ansatz is constructed.

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.