1996/11/30 by Ángel Ballesteros, Angel Ballesteros, Francisco J. Herranz +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #q-alg
paper · pdf · doi:10.1088/0305-4470/30/19/018
published as J.Phys. A30 (1997) 6797-6809 · 21 pages, LaTeX; two new references added
arxiv created 1997/01/27 · openalex publication_date 1997/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A Gelfan'd - Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of which directly provides its infinite- and finite-dimensional irreducible representations. Tensor product decompositions are worked out for some examples. Relations between contraction methods and boson realizations are also explored in several contexts. So, a class of two-boson representations for the non-standard deformation of is introduced and contracted to the non-standard quantum (1 + 1) Poincaré representations. Likewise, a quantum extended Hopf algebra is constructed and non-standard quantum oscillator algebra representations are obtained from it by means of another contraction procedure.