In algebra, Solomon's descent algebra of a Coxeter group is a subalgebra of the integral group ring of the Coxeter group, introduced by .
In the special case of the symmetric group S<sub>n</sub>, the descent algebra is given by the elements of the group ring such that permutations with the same descent set have the same coefficients. (The descent set of a permutation ÃÂ consists of the indices i such that ÃÂ(i) > ÃÂ(i+1).) The descent algebra of the symmetric group S<sub>n</sub> has dimension 2<sup>n-1</sup>. It contains the peak algebra as a left ideal.