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

TL;DR

This paper explores the algebraic structure of parabosonic algebra, establishing super-Hopf and Hopf algebra structures through alternative bosonisation methods, contributing to the mathematical understanding of parabosonic systems.

Contribution

It introduces two new variants of parabosonic algebra with established Hopf algebra structures, offering an alternative approach to bosonisation without relying on Lie superalgebraic structures.

Findings

Super-Hopf algebraic structure of parabosonic algebra established

Two variants of parabosonic algebra with Hopf algebra structures presented

Alternative bosonisation methods developed for parabosonic algebra

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.