Hai Xia XU(1);Cai Hui LU(2)
The paper discusses the structure of derivation algebra of infinite dimensional Lie algebra L(α,β). There are three cases:(1) If α and β are linearly independent over Q , then Der L(α,β)= C D f 0 C D g 0 ad L(α,β), where theD f 0 and D g 0 are derivations deterimined by the functions f 0 and g 0, f 0 and g 0 are linear functions defined on Z × Z ;(2) When α and β are linearly dependent over Q and not zero at the same time we have Der L(α,β) Der L(α′ ,0), (α′≠ 0), Der L(α,0) = C D -α 0 C D -α g 0 C D f 0 ad L(α,0) (α≠ 0), where D -α 0 is a fixed derivation, D -α g 0 and D f 0 are derivations determined by the functions g 0 and f 0;(3) If α=β=0, then Der L(0,0)= C D f 0 C D g 0 ad L(0,0).
