Reductive Algebraic Group

A reductive algebraic group is a type of mathematical object used to study symmetry in algebraic structures. Think of it as a set of transformations that preserve certain properties of geometric or algebraic objects, like rotations and reflections that leave shapes unchanged. These groups are "reductive," meaning they don't have complicated, hidden parts called unipotent elements, making their structure more manageable. They appear in areas like geometry, number theory, and physics, helping mathematicians understand symmetrical patterns, conservation laws, and fundamental symmetries in various systems.