Algebraic group theory

Algebraic group theory studies mathematical structures called algebraic groups, which combine algebraic equations with symmetry concepts. These groups consist of solutions to polynomial equations that also allow operations like multiplication and inversion, much like numbers or matrices. They help us understand symmetry in geometry, number theory, and other areas by analyzing how these elements behave and interact under algebraic rules. Essentially, algebraic group theory links algebraic equations with symmetry patterns, providing a framework for examining complex mathematical structures in a unified way.