Bannai-Ito algebras and the $osp(1,2)$ superalgebra

TL;DR

This paper explores the structure and representations of the Bannai-Ito algebra derived from the $osp(1,2)$ superalgebra, highlighting its algebraic properties and potential physical applications.

Contribution

It introduces the Bannai-Ito algebra $B(n)$, details its structure relations, and discusses its representations and realizations as symmetry algebras in physical models.

Findings

Defined the Bannai-Ito algebra $B(n)$ from $osp(1,2)$ tensor products.

Presented the algebra's structure relations.

Discussed physical model realizations.

Abstract

The Bannai-Ito algebra $B(n)$ of rank $(n-2)$ is defined as the algebra generated by the Casimir operators arising in the $n$-fold tensor product of the $osp(1,2)$ superalgebra. The structure relations are presented and representations in bases determined by maximal Abelian subalgebras are discussed. Comments on realizations as symmetry algebras of physical models are offered.