摘要
设p≠1为任意取定的正整数,q≠1为p次本原单位根.再设Γ1=(pZ)2\{(0,0)},Γ2=Z2\(pZ)2.记B=spanC{Lm,n|(m,n)∈Γ1■Γ2}为量子环面Cq[x±1,y±1]上的斜导子李代数,其中,基元满足的李关系为:当(m,n),(r,s)∈Γ2时,[Lm,n,Lr,s]=(qnr-qms)Lm+r,n+s;否则[Lm,n,Lr,s]=(nr-ms)Lm+r,n+s.本文给出了B的一个标准不变对称双线性型1ψ,并通过计算得到,李代数B的不变对称双线性型都是ψ1的常数倍.作者进一步证明了斜导子李代数B的系数在一维平凡表示C中的Leibniz二上同调群和它的二上同调群相同,即有HL2(B,C)=H2(B,C).
Let p≠ 1 be a positive integer, and q≠ 1 be a p-th primitive root of unity. Let Γ1=（pZ）^2／{（0.0））,Γ2=Z^2／（pZ）^2.Denote B= spanc B=spanc{Lm.n｜（m,n）∈Γ1UΓ2} the skew derivation Lie algebra over the quantum torus Cq[x^±1,y±1]. The Lie bracket is given by[Lm,n,Lr,s]=（nr-ms）Lm＋r,n＋s if （m,n）,（r,s）∈Γ2 ,and[Lm,n,Lr,s]=（nr-ms）Lm＋r,n＋s, in other cases. In this paper,the author first gave a standard invariant symmetric bilinear form φ1 of B,and then obtained that any invariant symmetric bilinear form of B is a multiple of φ1. In section two,the author proved that the Leibniz second cohomology group of B with coefficients in the 1-dimensional trivial representation C is equal to the second cohomology group of B,i. e. , HL^2 （B, C）= H^2 （B,C）.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第6期777-781,共5页
Journal of Xiamen University：Natural Science
基金
国家自然科学基金(10671160)资助
