Finite-dimensional irreducible modules of the Bannai--Ito algebra at characteristic zero
| Autor: | Huang, Hau-Wen |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11005-020-01306-9 |
| Popis: | Assume that $\mathbb F$ is an algebraically closed with characteristic $0$. The Bannai--Ito algebra $\mathfrak{BI}$ is a unital associative $\mathbb F$-algebra generated by $X,Y,Z$ and the relations assert that each of \begin{gather*} \{X,Y\}-Z, \qquad \{Y,Z\}-X, \qquad \{Z,X\}-Y \end{gather*} 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. Comment: The paper is to correct the main result of Communications in Algebra 44 (2016), 919-943; the paper arXiv:1910.11446 is to correct the main result of Communications in Algebra 47 (2019), 1869-1891 |
| Databáze: | arXiv |
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