Gradings, Braidings, Representations, Paraparticles: Some Open Problems

Axioms

关键词: paraparticles;    relative paraparticle sets;    universal enveloping algebras;    Lie (super)algebras;    ϑ-colored G-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;   

DOI  :  10.3390/axioms1010074

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.