Reductive groups

Reductive groups are mathematical structures in algebra that describe symmetries with a certain "nice" behavior. They are groups, meaning sets of elements with an operation combining them, and have properties allowing for a well-understood classification, especially over fields like the real or complex numbers. These groups don't have complicated or “nilpotent” components, making their structure easier to analyze and understand. Examples include familiar matrix groups like the special linear group. They are important in areas like geometry, number theory, and physics because they help study symmetrical systems with stable, manageable properties.