Hecke algebra of a locally compact group

The Hecke algebra of a locally compact group is a mathematical construction that arises primarily in representation theory and harmonic analysis, particularly in the study of groups and their representations. It plays a significant role in various areas, including number theory, algebraic geometry, and the theory of automorphic forms. ### Definition: For a locally compact group \( G \), the Hecke algebra is typically defined in relation to a set of subsets of \( G \), often associated with subgroups of \( G \).