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Finite-dimensional irreducible modules of the Bannai–Ito algebra at characteristic zero
Letters in Mathematical Physics ( IF 1.3 ) Pub Date : 2020-07-02 , DOI: 10.1007/s11005-020-01306-9
Hau-Wen Huang

Assume that $${\mathbb {F}}$$ F is algebraically closed with characteristic 0. A central extension $${\mathfrak {BI}}$$ BI of the Bannai–Ito algebras is a unital associative $${\mathbb {F}}$$ F -algebra generated by X , Y , Z , and the relations assert that each of $$\begin{aligned} \{X,Y\}-Z, \quad \{Y,Z\}-X, \quad \{Z,X\}-Y \end{aligned}$$ { X , Y } - Z , { Y , Z } - X , { Z , X } - Y is central in $${\mathfrak {BI}}$$ BI . In this paper, we classify the finite-dimensional irreducible $${\mathfrak {BI}}$$ BI -modules up to isomorphism. As we will see, the elements X , Y , Z are not always diagonalizable on finite-dimensional irreducible $${\mathfrak {BI}}$$ BI -modules.

中文翻译:

Bannai-Ito 代数在特征零处的有限维不可约模

假设 $${\mathbb {F}}$$ F 是代数闭的,特征为 0。 Bannai-Ito 代数的中心扩展 $${\mathfrak {BI}}$$ BI 是一个单位结合 $${\ mathbb {F}}$$ F -由 X , Y , Z 生成的 F -代数,以及关系断言 $$\begin{aligned} \{X,Y\}-Z, \quad \{Y,Z\ }-X, \quad \{Z,X\}-Y \end{aligned}$$ { X , Y } - Z , { Y , Z } - X , { Z , X } - Y 位于 $$ 的中心{\mathfrak {BI}}$$ BI . 在本文中,我们将有限维不可约 $${\mathfrak {BI}}$$ BI 模块分类为同构。正如我们将看到的,元素 X 、 Y 、 Z 并不总是在有限维不可约 $${\mathfrak {BI}}$$ BI 模块上对角化。
更新日期:2020-07-02
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