Stable Subalgebras of Lie Algebras and Associative Algebras

摘要

A subalgebra S of a Lie algebra L = (V, micro) is stable if S remains a subalgebra under small deformations of L. It is shown that S is stable if H(2)(S,V) = O. In particular, a semi-sample subalgebra of a Lie algebra is stable. The proof uses primarily the implicit function theorem. The proof is extended to the case of Lie algebras over algebraically closed fields and to associative algebras. (Author)