Bannai–Ito algebras and the universal R-matrix of osp(1|2) - Archive ouverte HAL Access content directly
Journal Articles Letters in Mathematical Physics Year : 2020

Bannai–Ito algebras and the universal R-matrix of osp(1|2)

Abstract

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.

Dates and versions

hal-02890130 , version 1 (06-07-2020)

Identifiers

Cite

Nicolas Crampé, Luc Vinet, Meri Zaimi. Bannai–Ito algebras and the universal R-matrix of osp(1|2). Letters in Mathematical Physics, 2020, 110 (5), pp.1043-1055. ⟨10.1007/s11005-019-01249-w⟩. ⟨hal-02890130⟩
75 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More