单李代数C_q:=C_q[t_1^(±1),t_2^(±1),t_3^(±1),t_4^(±1)]/C的自同构群  

Automorphism Group of Simple Lie Algebra C_q:=C_q[t_1^(±1),t_2^(±1),t_3^(±1),t_4^(±1)]C

作　　者：黄忠铣[1] 

机构地区：[1]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《武夷学院学报》2013年第2期43-46,共4页Journal of Wuyi University

基　　金：福建省科技重点项目(项目编号:2011Y0049)

摘　　要：q-量子环面Cq:=Cq[t1±1,t2±1,t3±1,t4±1]是复数域C上由t1±1,t2±1,t3±1,t4±1生成的有单位元的结合代数,并满足定义关系titj=qijtjti,titi-1=ti-1ti=1,其中矩阵q=(qij)∈M4×4(C)有qii=1,qij=q-1ji.基于当q21,q31,q23分别为p,q,r次本原单位根(其中p,q,r为互质的正整数)时,研究一类单结合代数Cq[t1±1,t2±1,t3±1,t4±1]的自同构和反自同构,决定单李代数CqC的自同构群.The quantum torus Cq：=Cq[t1^（±1）,t2^（±1）,t3^（±1）,t4^（±1）C is the unital associative algebra over the complex number field generated by t1±1,t2±1,t3±1,t4±1 and subject to the defining relations titj=qijtjti and titi-1=ti-1ti=1 ,where the matrix q=（qij）∈M4×4（C） with qii=1 and qij=qij-1.In this paper, under the condition that q21,q31,q23 are the primitive p-th,q-th,r-th roots of unity respectively （p,q,r are coprime positive integers.）,the automorphisms and antiautomorphisms of a class of simple associative algebra Cq[t1^±1,t2^±1,t3^±1,t4^±1]C are studied, then the automorphism group of a class of simple Lie algebra CqC are determined.

关 键 词：q-量子环面 自同构群 矩阵 

分 类 号：O152.5[理学—数学]