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Axioms 2012, 1(1), 74-98; doi:10.3390/axioms1010074

Gradings, Braidings, Representations, Paraparticles: Some Open Problems

School of Mathematics, Aristotle University of Thessaloniki (AUTH), Thessaloniki 54124, Greece
Received: 9 April 2012 / Revised: 4 June 2012 / Accepted: 4 June 2012 / Published: 15 June 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
View Full-Text   |   Download PDF [541 KB, 18 June 2012; original version 15 June 2012]

Abstract

A research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings and braided group structures present in the various parastatistical algebraic models. The second part of the proposal aims at refining and utilizing a previously published methodology for the study of the Fock-like representations of the parabosonic algebra, in such a way that it can also be directly applied to the other parastatistics algebras. Finally, in the third part, a couple of Hamiltonians is proposed, suitable for modeling the radiation matter interaction via a parastatistical algebraic model.
Keywords: paraparticles; relative paraparticle sets; universal enveloping algebras; Lie (super)algebras; -colored -graded Lie algebras; braided groups; graded Hopf algebras; braided (graded) modules; braided (graded) tensor products; braided and symmetric monoidal categories; quasitriangularity; R-matrix; bicharacter; color function; commutation factor paraparticles; relative paraparticle sets; universal enveloping algebras; Lie (super)algebras; -colored -graded Lie algebras; braided groups; graded Hopf algebras; braided (graded) modules; braided (graded) tensor products; braided and symmetric monoidal categories; quasitriangularity; R-matrix; bicharacter; color function; commutation factor
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Kanakoglou, K. Gradings, Braidings, Representations, Paraparticles: Some Open Problems. Axioms 2012, 1, 74-98.

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