完备Lie代数的若干进展

Some Advances on Complete Lie Algebras

近十年来，特别是近几年完备Ｌｉｅ代数的研究取得了许多进展，本文分以下六个方面介绍这一领域的研究状况．０）引言；１）完备Ｌｉｅ代数的分解和唯一性；２）一些完备Ｌｉｅ代数；３）可解完备Ｌｉｅ代数；４）完备Ｌｉｅ代数的极大环面子代数，Ｋｉｌｉｎｇ型及结构；５）一些公开问题．

In recent years, there are many advances in the study on the complete Lie algebras. In this paper, we present the following aspects of these advances: the decomposition of complete Lie algebra and its uniqueness, some complete Lie algebras, solvable complete Lie algebras and the maximal toral subalgebras, Killing forms and construction of complete Lie algebras. At last, we propose some open problems.