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Gradings, Braidings, Representations, Paraparticles: Some Open Problems
School of Mathematics, Aristotle University of Thessaloniki (AUTH), Thessaloniki 54124, Greece
Received: 9 April 2012; in revised form: 4 June 2012 / Accepted: 4 June 2012 / Published: 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
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Kanakoglou, K. Gradings, Braidings, Representations, Paraparticles: Some Open Problems. Axioms 2012, 1, 74-98.
Kanakoglou K. Gradings, Braidings, Representations, Paraparticles: Some Open Problems. Axioms. 2012; 1(1):74-98.
Kanakoglou, Konstantinos. 2012. "Gradings, Braidings, Representations, Paraparticles: Some Open Problems." Axioms 1, no. 1: 74-98.