%0 Journal Article
%T Bannai–Ito algebras and the universal R-matrix of osp(1|2)
%+ Institut Denis Poisson (IDP)
%+ Laboratoire Charles Coulomb (L2C)
%+ Centre de Recherches Mathématiques [Montréal] (CRM)
%A Crampé, Nicolas
%A Vinet, Luc
%A Zaimi, Meri
%Z The research of L. Vinet is supported in part by a Discovery Grant from the Natural Science and Engineering Research Council (NSERC) of Canada.
%Z M. Zaimi holds a NSERC graduate scholarship.
%Z 10 pages, 15 ref.
%< avec comité de lecture
%@ 0377-9017
%J Letters in Mathematical Physics
%I Springer Verlag
%V 110
%N 5
%P 1043-1055
%8 2020-05
%D 2020
%Z 1909.06426
%R 10.1007/s11005-019-01249-w
%Z Mathematics [math]/Representation Theory [math.RT]
%Z Mathematics [math]/Mathematical Physics [math-ph]Journal articles
%X The Bannai-Ito algebra BI(n) is viewed as the centralizer of the action of osp(1|2) in the n-fold tensor product of the universal algebra of this Lie superalgebra. The generators of this centralizer are constructed with the help of the universal R-matrix of osp(1|2). The specific structure of the osp(1|2) embeddings to which the centralizing elements are attached as Casimir elements is explained. With the generators defined, the structure relations of BI(n) are derived from those of BI(3) by repeated action of the coproduct and using properties of the R-matrix and of the generators of the symmetric group Sn.
%G English
%L hal-02890130
%U https://hal.science/hal-02890130
%~ UNIV-TOURS
%~ CNRS
%~ UNIV-ORLEANS
%~ L2C
%~ TDS-MACS
%~ MIPS
%~ UNIV-MONTPELLIER
%~ IDP
%~ UM-2015-2021
%~ TEST3-HALCNRS