Conjugacy results for the Lie algebra si_2 over an algebra which is a UFD

摘要

Let F be a field of characteristic not 2 and assume all algebras are over F. We establish several conjugacy theorems for the special linear Lie algebra sfe over an F-algebra which is a UFD. We find the structure of the full automorphism group as well as conditions for when two such algebras are isomorphic. The structure of theii derivation algebras is also discussed Often we work with more general coordinates when this is feasible.