量子环面上斜导子李代数的自同构群

The Automorphism Group of Skew Derivation Lie Algebra over Quantum Tori

Kirkman,Procesi,Small等人计算了量子环面Cq[X,Y,X-1,Y-1]的导子和它的自同构群.特别令人感兴趣的是姜翠波和孟道冀所做的关于Cq[X,Y,X-1,Y-1]的导子李代数(即Virasoro like代数的 q 类似)以及 Virasoro like代数的导子李代数及其自同构群的相关结果.他们清楚的刻画了自同构群的结构.受前述工作的启发,我们研究了量子环面上斜导子李代数上的自同构群的结构,并显式的给出了其自同构的具体表达式.这样本文就推广了姜和孟的主要结果.

Kirkman E,Procesi C and Small L A computed the derivations of C_q[X,Y] and the automorphism group of C_1[X,Y,X^(-1),Y^(-1)].What is the most interesting to us is the work of Jiang Cuibo and Meng Daoji,they studied the Virasoro-like algebra and its q-analog’s automorphism groups,and found that they have the same structure.It’s known,Viraso-like algebra and its q-analog can be regarded as two special cases of skew derivation Lie algebra of quantum toridal.In this paper,we will study the structure of this kind of Lie algebra,and obtained the formula of the automorphism.