Hecke algebra

A Hecke algebra is a mathematical structure that arises from studying symmetries and transformations within certain geometric spaces or algebraic systems. It involves a set of operations that combine and relate these symmetries in a way that captures their intricate patterns, often encoded with parameters reflecting underlying geometric or number-theoretic properties. Hecke algebras are fundamental in areas like representation theory, number theory, and the study of automorphic forms, providing a framework to analyze how symmetries behave and interact in complex mathematical contexts.