W(a,b)型李代数是 Witt代数和它的密度张量模的半直积,很多无限维李代数都具有这种结构。这类李代数的结构和表示被广泛的研究。通过计算一类W (0,1)李代数的二维中心扩张P 的导子代数,确定它有四个外导子。在文献[1]中,李代数只有2个外导子,而我们得到了一个李代数的中心扩张的导子代数与其导子代数不同构的例子。%W(a,b)Lie algebra is the semi direct product of Witt algebra and its density tensor module.Many infinite dimensional Lie algebras have this algebraic structure.The structure theory and representation theory ofW(a,b)Lie algebra have been investigated by many authors recently.In this pa-per,we calculate the derivations of the Lie algebra P,which are the two dimensional central extensions ofW(0,1).Our study shows that P has four outer derivations.In [1],it is provedW(a,b)Lie algebra has only two outer derivations.Then we obtain one example that the derivation algebra of the central ex-tensions of Lie algebra is not isomorphic to that of the Lie algebra.
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