On Structure Of Lie Algebras Over Quantum Torus

Let q be a generic,C_q:=C_q[x₁^±1,x₂^±1]be the correspondingquantum torus．D(C_q)the set of derivations of C_q and C_q^*=C_qï¼¼C^*．Set L^q=C_q^*(?)D(C_q),then under the usual Lie product L_q becomesa Lie algebra．Indeed this Lie algebra is isomophic to the Liealgebra generated by the symbols E(m),x^m and d₁,d₂ subject tothe following anti-symmetric relations:where m=(m₁,m₂),n=(n₁,n₂)∈Γ^*=Z²ï¼¼{0},Let L'_q be the derived Lie subalgebra of L_q．In this paper,westudy the automorphism group,universal central extension andderivations of the Lie algebra L'_q．...