Graded structure and Hopf structures in parabosonic algebra. An alternative approach to bosonisation

Abstract

Parabosonic algebra in infinite degrees of freedom is presented as a generalization of the bosonic algebra, from the viewpoints of both physics and mathematics. The notion of super-Hopf algebra is shortly discussed and the super-Hopf algebraic structure of the parabosonic algebra is established (without appealing to its Lie superalgebraic structure). Two possible variants of the parabosonic algebra are presented and their (ordinary) Hopf algebraic structure is estabished: The first is produced by "bosonising" the original super-Hopf algebra, while the second is constructed via a slightly different path.

12 pages, Talk presented at the International Conference: "New techniques in Hopf algebras and graded ring theory", Brussels, September 19-23, 2006. Submitted for publication at the proceedings

References in corpus (3)

• Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map
• Bosonisation and Parastatistics: An Example and an Alternative Approach
• Parabosonic and parafermionic algebras. Graded structure and Hopf structures

Cited by in corpus (2)

• From $s{l}_q(2)$ to a Parabosonic Hopf Algebra
• Gradings, Braidings, Representations, Paraparticles: some open problems