The Derivation Algebra of the Schrdinger-Virasoro Lie Algebra

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 Schrdinger-Virasoro Lie algebra L,which is the universal central extension of the Schrdinger-Virasoro Lie algebra sv with one-dimensional center.It is proved that L has only one outer derivation,while sv has three outer derivations.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.