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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 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.
==References==
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