Algebraic groups

Algebraic groups are mathematical structures that combine concepts from algebra and geometry. They consist of sets of points, such as those defined by polynomial equations, that also have a group operation (like combining numbers). This operation must satisfy certain rules, similar to how addition or multiplication works. Algebraic groups help mathematicians study symmetry and transformations in various fields, including number theory, geometry, and even physics. They provide a framework for understanding how different mathematical objects relate to one another in a structured way.