Bosonisation and Parastatistics: An Example and an Alternative Approach

Abstract

Definitions of the parastatistics algebras and known results on their Lie (super)algebraic structure are reviewed. The notion of super-Hopf algebra is discussed. The bosonisation technique for switching a Hopf algebra in a braided category ${}_H\mathcal{M}$ ($H$: a quasitriangular Hopf algebra) into an ordinary Hopf algebra is presented and it is applied in the case of the parabosonic algebra. A bosonisation-like construction is also introduced for the same algebra and the differences are discussed.

13 pages, Contribution to "AGMF: Algebra, Geometry, and Mathematical Physics", Baltic-Nordic Workshop: Lund, 12-14 October, 2006

References in corpus (1)

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

Cited by in corpus (2)

• 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