Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map

Abstract

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie algebras using the parabosonic (and parafermionic) extension of the Jordan Schwinger map. The differences between the Hopf algebraic and the graded Hopf superalgebraic structure on the parabosonic algebra are discussed.

11 pages, LaTex2e file

References in corpus (1)

• A q-deformation of the parastatistics and an alternative to the Chevalley description of $U_q[osp(2n+1/2m)]$

Cited by in corpus (15)

• The Bannai-Ito algebra and some applications
• A Laplace-Dunkl equation on $S^2$ and the Bannai-Ito algebra
• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)
• Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras
• Super-Hopf realizations of Lie Superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map
• The quantum superalgebra ${\mathfrak{osp}}_q(1|2)$ and a $q$-generalization of the Bannai-Ito polynomials
• Interpretation and Extension of the Green's Ansatz for Paraparticles
• Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras
• Graded structure and Hopf structures in parabosonic algebra. An alternative approach to bosonisation
• Bosonisation and Parastatistics: An Example and an Alternative Approach
• Gradings, Braidings, Representations, Paraparticles: some open problems
• Parabosonic and parafermionic algebras. Graded structure and Hopf structures
• Variants of bosonisation in Parabosonic algebra. The Hopf and super-Hopf structures
• Generalized exclusion and Hopf algebras