一类量子环面李代数的自同构群

Automorphism Group for a Class of Lie Algebras Over Quantum Torusy

记C_q=C_q[t_1^(±1),t_2^(±1)]为复数域上的非交换环面结合代数,q≠0为非单位根,DerC_q=adC_q⊕D_2为C_q的导子李代数,其中adC_q为C_q的内导子李代数,Cd_1,Cd_2为C_q的度导子.本文研究李代数C_q\C,L=C_q\C⊕Cd_1⊕Cd_2,L=C_q\C⊕adC_q⊕Cd_1⊕Cd_2及Weyl-型代数C[D_2]的自同构群.

Let Cq = Cq[x1^（±1）,x2^（±1）]（q^n≠1,n∈N） be the non-commutative torus over the complex field,DerCq = adCq ⊕ D2 is the derivation algebra group of Cq,where adCq is inner dreivation algebra of Cq,Cd1,Cd2 are the degree derivations of Cq.In this paper,we study the automorphism groups for Lie algebraCq／C,L =Cq／C⊕Cd1 ⊕Cd2,L=Cq／⊕⊕ad⊕q⊕⊕d1⊕Cd2 and Weyl-type algebraC[D2].