一类Schrdinger-Virasoro李代数的导子代数(英文)

The Derivation Algebra of the Schrdinger-Virasoro Lie Algebra

对于中心非零的perfect李代数,关于它的泛中心扩张的导子代数与它本身的导子代数之间的关系尚未有一个一般的结论.通过计算带有一维中心的Schrdinger-Virasoro李代数sv的泛中心扩张L的导子,证明了L只有一个外导子,而由文献[1]知sv有三个外导子,从而得到了一个中心非零的perfect李代数的导子代数与其泛中心扩张的导子代数不同构的例子.

For the perfect Lie algebra with one - dimensional center at lest, there is not a general result about the relationship between its derivation algebra and that of its universal central extension. In this paper, we determine the derivation algebra of the Schrodinger - Virasoro Lie algebra L, which is the universal central extension of the Schrodinger - Virasoro Lie algebra with one - dimensional center. It is proved that has only one outer derivation, while has three outer derivations [1]. Hence, we get one example that the derivation algebra of the universal central extension of a Lie algebra, the center of which is not zero, is not isomorphism to that of the Lie algebra.