Higher order peak algebras

Representation theory of the higher-order peak algebras

The representation theory (idempotents, quivers, Cartan invariants, and Loewy series) of the higher-order unital peak algebras is investigated. On the way, we obtain new interpretations and generating functions for the idempotents of descent algebras introduced in Saliola (J. Algebra 320:3866, 2008).

Unital Versions of the Higher Order Peak Algebras

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.].

SOME CHARACTERIZATIONS OF HYPER MV -ALGEBRAS

In this paper we characterize hyper MV -algebras in which 0 or1 are scalar elements . We prove that any nite hyper MV -algebra that 0is a scaler element in it, is an MV -algebra. Finally we characterize hyperMV -algebras of order 2 and order 3.

On Higher Order Bourgain Algebras of a Nest Algebra

Following earlier work in which we provided algebraic characterizations of the right, left, and two-sided Bourgain algebras, as well as the second order Bourgain algebras, associated with a nest algebra, we herein demonstrate that a given nest algebra has (essentially) at most six different third order Bourgain algebras, and that every fourth order (or higher) Bourgain algebra of the nest algeb...

Prime Higher Derivations on Algebras