  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 sl_2
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. We also study the structure of their derivation algebras. Often we
work with more general coordinates when this if feasible.
