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ABSTRACT
In this paper, we discuss compatible left-symmetric algebra structures on some complete Lie algebras, and as an application, we obtain all the derivations of such left-symmetric algebras.
ACKNOWLEDGMENTS
We are grateful for Professor E.I. Zelmanov, Professor H.C. Myung and the referees for very useful suggestion. This work was supported in part by the National Natural Science Foundation of China, Mathematics Tianyuan Foundation, the Project for Young Mainstay Teachers and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China. The first author also thanks the invitation of Asia Pacific Center for Theoretic Physics in Korea.