CLASSIFICATION OF IRREDUCIBLE BOUNDED WEIGHT MODULES OVER THE DERIVATION LIE ALGEBRAS OF QUANTUM TORI
CLASSIFICATION OF IRREDUCIBLE BOUNDED WEIGHT MODULES OVER THE DERIVATION LIE ALGEBRAS OF QUANTUM TORI
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DOI：
10.1016/j.laa.2016.01.009
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发表时间：
2015-06
影响因子：
1.1
通讯作者：
Genqiang Liu;K. Zhao
中科院分区：
文献类型：
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作者：
Genqiang Liu;K. Zhao
设d> 1是一个整数，q=（q i j）d× d是一个d× d复矩阵，满足q i i= 1，q i j= q j i− 1且所有q i j都是单位根。设Cq是与q相关联的有理量子环面代数，Der（Cq）是它的导子李代数.本文给出了Der（Cq）上不可约有界权模的一个完全分类.它们是Der（C q）-模V α（V，W）的不可约子商，对于有限维不可约gl d-模V、有限维Γ-分次不可约gl N-模W和α∈ C d，其中整数N由q唯一确定。
Let d> 1 be an integer, q=(q i j) d× d a d× d complex matrix satisfying q i i= 1, q i j= q j i− 1 with all q i j being roots of unity. Let C q be the rational quantum torus algebra associated with q, and Der (C q) its derivation Lie algebra. In this paper, we give a complete classification of irreducible bounded weight modules over Der (C q). They turn out to be irreducible sub-quotients of Der (C q)-module V α (V, W) for a finite dimensional irreducible gl d-module V, a finite dimensional Γ-graded-irreducible gl N-module W, and α∈ C d where the integer N is uniquely determined by q.