Geodesic
Unital versions of the higher order peak algebras
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411―430], and show that they can be obtained as homomorphic images of certain subalgebras of the Mantaci-Reutenauer algebras of type $B$. This generalizes a result of Bergeron, Nyman and the first author [Trans. AMS 356 (2004), 2781―2824]. 
@article{DMTCS_2009_special_256_a51,
     author = {Aguiar, Marcelo and Novelli, Jean-Christophe and Thibon, Jean-Yves},
     title = {Unital versions of the higher order peak algebras},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2729},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2729/}
}
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%V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
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Aguiar, Marcelo; Novelli, Jean-Christophe; Thibon, Jean-Yves. Unital versions of the higher order peak algebras. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2729. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2729/

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