一类量子环面李代数的单性(英文)  

Simplicity of a Class of Quantum Torus Lie Algebras

作　　者：罗柳红[1] 卢才辉[2] 

机构地区：[1]北京林业大学理学院,北京100083 [2]首都师范大学数学科学学院,北京100037

出　　处：《数学进展》2012年第2期139-149,共11页Advances in Mathematics（China）

摘　　要：令C_q:=C_q[t_1^(±1),t_2^(±1),t_3^(±1)]为量子环面结合代数,L_q=C_q/C为量子环面李代数。本文定义了一个与q=(qij)_(i,j=1)~3相关的指数方程体系,称之为C_q的特征方程组。通过这个特征方程组,证明了L_q是非单的当且仅当特征方程组在Z^3中有非零解。对于|q|=0,证明了在C_q中存在一个极大交换子代数I,并且I严格包含中心Z(C_q)。同时文中也指出,对于|q|≠0,在C_q中不存在这样的子代数。Let C_q：= C_q[t_1^（±1）,t_2^（±1）,t_3^（±1）]be the quantum torus associative algebra and L_q = C_q/C be the quantum torus Lie algebra.In this article we define a system of exponential equations associated to q =（qij）_（i,j）~3=1 and call it characteristic equations of C_q,and we prove that L_q is not simple if and only if the characteristic equations have nonzero solution in Z^3.For ｜q｜ = 0,we show that there exists a maximal Abelian subalgebra I in C_q such that I strictly contains the center Z（C_q）.We also point out that such a subalgebra does not exist in C_q for ｜q｜≠0.

关 键 词：李代数 量子环面 单性 

分 类 号：O152.5[理学—数学]