STABLE SUBALGEBRAS OF LIE ALGEBRAS AND ASSOCIATIVE ALGEBRAS.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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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 H2S,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
- Theoretical Mathematics