Abstract
Assume that \({\mathbb {F}}\) is algebraically closed with characteristic 0. A central extension \({\mathfrak {BI}}\) of the Bannai–Ito algebras is a unital associative \({\mathbb {F}}\)-algebra generated by X, Y, Z, and the relations assert that each of
is central in \({\mathfrak {BI}}\). In this paper, we classify the finite-dimensional irreducible \({\mathfrak {BI}}\)-modules up to isomorphism. As we will see, the elements X, Y, Z are not always diagonalizable on finite-dimensional irreducible \({\mathfrak {BI}}\)-modules.
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The research is supported by the Ministry of Science and Technology of Taiwan under the project MOST 106-2628-M-008-001-MY4.
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Huang, HW. Finite-dimensional irreducible modules of the Bannai–Ito algebra at characteristic zero. Lett Math Phys 110, 2519–2541 (2020). https://doi.org/10.1007/s11005-020-01306-9
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DOI: https://doi.org/10.1007/s11005-020-01306-9