Typed binary trees and generalized dendrifom algebras
type: Item
instance of: scholarly article
title: Typed binary trees and generalized dendrifom algebras
zbMATH Open document ID: 1478.16028
published in: Journal of Algebra
publication date: 2021-08-25T00:00:00Z
review text: Dendriform algebras are associative algebras with an associativity splitting, that is to say their associative product can be written as a sum of two products subject to some axioms. Classical examples of dendriform algebras are given by shuffle algebras. Other examples include the dendriform algebras based on binary tries, on \(\Omega\)-typed binary tries (i.e., on trees with a map from this set of edges to some set \(\Omega\)). The aim in the article is to give both a unification and a generalization of the extended dendriform structures. A notion of an \(\Omega\)-dendriform algebra is introduced. The constructed objects are studied also from a Hopf-algebraic and a combinatorial point of view.
Mathematics Subject Classification ID: 16T30
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 7385158
zbMATH Keywords: dendriform algebra
zbMATH Keywords: diassociative semigroup
zbMATH Keywords: plane binary trees
zbMATH Keywords: shuffle product
author: Loïc Foissy
reviewed by: Dmitry Artamonov
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2021.06.025
OpenAlex ID: W3006684619
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DOI: 10.1016/J.JALGEBRA.2021.06.025
description: scientific article; zbMATH DE number 7385158