Examples
Since, is a linear algebraic group. The embedding 
shows that is a unipotent group.
The deeper structure theory applies to connected linear algebraic groups G, and begins with the definition of Borel subgroups B. These turn out to be maximal as connected solvable subgroups (i.e., subgroups with composition series having as factors one-dimensional subgroups, all of which are groups of additive or multiplicative type); and also minimal such that G/B is a projective variety.
The most important subgroups of a linear algebraic group, besides its Borel subgroups, are its tori, especially the maximal ones (similar to the study of maximal tori in Lie groups). If there is a maximal torus which splits (i.e. is isomorphic to a product of multiplicative groups), one calls the linear group split as well. If there is no splitting maximal torus, one studies the splitting tori and the maximal ones of them. If there is a rank at least 1 split torus in the group, the group is called isotropic and anisotropic if this is not the case. Any anisotropic or isotropic linear algebraic group over a field becomes split over the algebraic closure, so this distinction is interesting from the point of view of Algebraic number theory.
Read more about this topic: Linear Algebraic Group
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