1996/10/31 by Gaetano Fiore · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #hep-th #math.QA #q-alg
paper · pdf · doi:10.1063/1.532439
published as J.Math.Phys. 39 (1998) 3437-3452 · Latex file, 26 pages, no figures. Extended changes. Final Version to appear in J. Math. Phys
arxiv created 1998/01/08 · openalex publication_date 1998/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Any deformation of a Weyl or Clifford algebra 𝒜 can be realized through a “deforming map,” i.e., a formal change of generators in 𝒜. This is true in particular if 𝒜 is covariant under a Lie algebra g and its deformation is induced by some triangular deformation Uhg of the Hopf algebra Ug. We propose a systematic method to construct all the corresponding deforming maps, together with the corresponding realizations of the action of Uhg. The method is then generalized and explicitly applied to the case that Uhg is the quantum group Uhsl(2). A preliminary study of the status of deforming maps at the representation level shows in particular that “deformed” Fock representations induced by a compact Uhg can be interpreted as standard “undeformed” Fock representations describing particles with ordinary Bose or Fermi statistics.