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

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

2007-06-19

arxiv.org/abs/0706.2825v1

Physics

Mathematical Physics

12 pages, Talk presented at the International Conference: "New techniques in Hopf algebras and graded ring theory", Brussels,

Scientific paper

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.

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