Algebraic group

An algebraic group is a mathematical structure that combines symmetry and algebraic equations. It consists of a set of elements, like numbers or matrices, with an operation (such as addition or multiplication) that meets specific rules, like associativity, identity, and inverses. Additionally, the elements and operation are described using polynomial equations, linking algebra and geometry. Think of it as a system where symmetry transformations or solutions to equations form a smooth, continuous structure, allowing mathematicians to understand complex symmetries and solve problems across areas like geometry, physics, and number theory.