2008/02/26 by K. Kanakoglou, K Kanakoglou, C. Daskaloyannis +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structure #Algebraic structures and combinatorial models #Filtered algebra #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Quantum group #Quasitriangular Hopf algebra #Representation theory of Hopf algebras #Universal enveloping algebra #hep-th #math-ph #math.MP #math.RA #msc:16S40 #msc:16W30 #msc:57T05
paper · pdf · doi:10.1088/1751-8113/41/10/105203
published as J.Phys.A41:105203,2008 · 27 pages, some typos of the journal version are corrected and a couple of references added
openalex publication_date 2008/02/26 · arxiv created 2009/02/06 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Parabosonic algebra in finite or infinite degrees of freedom is considered as a -graded associative algebra, and is shown to be a -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2 n ) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category . The bosonization technique for switching a Hopf algebra in the braided monoidal category (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure.