## The Peak algebra of the symmetric group algebra

### Rosa Orellana, (Dartmouth College)

The peak algebra is a unital subalgebra introduced by
Aguiar-Bergeron-Nyman as the image of the descent
algebra of type B under the map that forgets signs.

A linear basis of the peak algebra is given by sums of
permutations with common peak set. By exploiting the
combinatorics of sparce subsets of $[n-1]$ and
compositions of $n$ called almost-odd and thin,
we construct three new linear bases of the peak algebra.

In this talk we use the above basses to describe the
Jacobson radical of the Peak algebra and to characterize
the elements of the Peak algebra in terms of its action on
the tensor algebra of a vector space.

Joint work with M. Aguiar and K. Nyman.

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