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

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...

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Bibliographic Details
Published in:arXiv.org 2009-01
Main Authors: Kanakoglou, K, Daskaloyannis, C
Format: Article
Language:English
Subjects:
Algebra
Bosons
Braiding
Quotients
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0901.4320