扭的Multi-loop代数的自同构群

Automorphism group of a twisted multi-loop algebra

设g是三维实李代数so(3)的复化李代数,A=C[t1±1,t2±1]是两个变量的复系数Laurent多项式环,设L(t1,t2,1)=gCA,d1,d2为L(t1,t2,1)的导子.在研究了L(t1,t2,1)的自同构群结构的基础上,研究L(t1,t2,1)(Cd1Cd2)的自同构群结构,证明其自同构群同构于C××C××GL2(Z).

Let g be the complexification of the real Lie algebra so（3） and A = C[t1± 1,t2± 1]be the Laurent polynomial algebra with two commuting variables.Let L（t1,t2,1） = gCA,d1,d2 are the derivations of L（t1,t2,1）.Basing on the work for the automorphism group of L（t1,t2,1）,we study the automorphism group of L（t1,t2,1） （Cd1Cd2）.It is proofed that the automorphism group is automorpic to C×× C×× GL2（Z）.