Unital versions of the higher order peak algebras

TL;DR

This paper constructs unital extensions of higher order peak algebras, linking them to subalgebras of Mantaci-Reutenauer algebras of type B, thus generalizing previous results.

Contribution

It introduces unital versions of higher order peak algebras as homomorphic images of specific subalgebras of Mantaci-Reutenauer algebras, expanding their algebraic framework.

Findings

Unital extensions of higher order peak algebras are constructed.

These algebras are realized as homomorphic images of subalgebras of Mantaci-Reutenauer algebras of type B.

The work generalizes previous algebraic results by Bergeron, Nyman, and others.

Abstract

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.].