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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