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

Gradings, Braidings, Representations, Paraparticles: Some Open Problems

Received: 9 April 2012; in revised form: 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)
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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

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

Chicago/Turabian Style

Kanakoglou, Konstantinos. 2012. "Gradings, Braidings, Representations, Paraparticles: Some Open Problems." Axioms 1, no. 1: 74-98.


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