Peak algebra

In mathematics, the peak algebra is a (non-unital) subalgebra of the group algebra of the symmetric group "S""n", studied by . It consists of the elements of the group algebra of the symmetric group whose coefficients are the same for permutations with the same peaks. (Here a peak of a permutation σ on {1,2...,"n"} is an index "i" such that σ("i"–1)<σ("i")>σ("i"+1).) It is a left ideal of the descent algebra. The direct sum of the peak algebras for all "n" has a natural structure of a Hopf algebra.