# Hecke algebra (disambiguation)

In mathematics, a **Hecke algebra** is classically the algebra of Hecke operators studied by Erich Hecke. It may also refer to one of several algebras (some of which are related to the classical Hecke algebra):

- Iwahori–Hecke algebra of a Coxeter group.
- Hecke algebra of a pair (
*g*,*K*) where*g*is the Lie algebra of a Lie group*G*and*K*is a compact subgroup of*G*. - Hecke algebra of a locally compact group
*H*(*G*,*K*), for a locally compact group*G*with respect to a compact subgroup*K*.- Hecke algebra of a finite group, the algebra spanned by the double cosets
*HgH*of a subgroup*H*of a finite group*G*. - Spherical Hecke algebra, when
*K*is a maximal open compact subgroup of a general linear group.

- Hecke algebra of a finite group, the algebra spanned by the double cosets
- Affine Hecke algebra
- Parabolic Hecke algebra
- Parahoric Hecke algebra

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