Algebraic groups

Algebraic groups are a central concept in an area of mathematics that blends algebra, geometry, and number theory. An algebraic group is defined as a group that is also an algebraic variety, meaning that its group operations (multiplication and inversion) can be described by polynomial equations. More formally, an algebraic group is a set that satisfies the group axioms (associativity, identity, and inverses) and is also equipped with a structure of an algebraic variety.