Classification of irreducible bounded weight modules over the derivation Lie algebras of quantum tori

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• 作者：Genqiang Liu^a ; ^{liugenqiang@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Kaiming Zhao^b ; ^c ; ^{kzhao@wlu.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：17B10 ; 17B20 ; 17B65 ; 17B66 ; 17B68
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：495
• 期：Complete
• 页码：11-23
• 全文大小：344 K

文摘

Let d>1$d>1$ be an integer, q=(q_ij)_d×d$q={(q_{ij})}_{d\times d}$ a e50b6e2a43c20e62e9f1d66606237c7c" title="Click to view the MathML source">d×d$d\times d$ complex matrix satisfying q_ii=1$q_{ii}=1$, $q_{ij}=q_{ji}^{-1}$ with all q_ij$q_{ij}$ being roots of unity. Let C_q${\mathbb{C}}_q$ be the rational quantum torus algebra associated with q  , and 16ee5b9c9786208858d242" title="Click to view the MathML source">Der(C_q)$\mathrm{Der}({\mathbb{C}}_q)$ its derivation Lie algebra. In this paper, we give a complete classification of irreducible bounded weight modules over 16ee5b9c9786208858d242" title="Click to view the MathML source">Der(C_q)$\mathrm{Der}({\mathbb{C}}_q)$. They turn out to be irreducible sub-quotients of 16ee5b9c9786208858d242" title="Click to view the MathML source">Der(C_q)$\mathrm{Der}({\mathbb{C}}_q)$-module V^α(V,W)${\mathcal{V}}^{\alpha }(V,W)$ for a finite dimensional irreducible gl_d${\mathfrak{gl}}_d$-module V  , a finite dimensional Γ-graded-irreducible gl_N${\mathfrak{gl}}_N$-module W  , and α∈C^d$\alpha \in {\mathbb{C}}^d$ where the integer N is uniquely determined by q.