Gradings, Braidings, Representations, Paraparticles: some open problems
arXiv:1210.2348
Abstract
A long-term 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, and their sutability for modeling the radiation matter interaction via a parastatistical algebraic model is discussed.
25 pages, some typos corrected
References in corpus (13)
- Gradings on the Albert Algebra and on
- Group Gradings on Simple Lie Algebras of Type "A"
- Paraboson quotients. A braided look at Green ansatz and a generalization
- Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map
- Graded Fock--like representations for a system of algebraically interacting paraparticles
- Group gradings on finitary simple Lie algebras
- Super-Hopf realizations of Lie Superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map
- Ladder operators, Fock-spaces, irreducibility and group gradings for the Relative Parabose Set algebra
- SL(3|N) Wigner quantum oscillators: examples of ferromagnetic-like oscillators with noncommutative, square-commutative geometry
- On a class of Fock-like representations for Lie Superalgebras
- Universal R-matrices for finite Abelian groups -- a new look at graded multilinear algebra
- Graded structure and Hopf structures in parabosonic algebra. An alternative approach to bosonisation
- Gradings on