Since a Lie algebra is also a vector space, we can see that a Lie algebra has variety structure.
Is the bracket a morphism of varieties, and if it isn't always the case, is there a name for a structure that does have that property?
- If a variety is also a group, where the multiplication and inverse are morphisms of varieties, we have an algebraic group.
- If a variety is also a Lie algebra, where the Lie bracket is a morphism of varieties. What do we call this?