Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests
type: Item
instance of: scholarly article
title: Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests
zbMATH Open document ID: 1482.17037
author: Yuanyuan Zhang
author: Zhicheng Zhu
author: Dan Chen
author: Jin-Wei Wang
published in: Open Mathematics
publication date: 2021-11-29T00:00:00Z
review text: A family Rota-Baxter is an algebra equipped with a family of operators \((R_\alpha)_{\alpha\in \Omega}\) indexed by a fixed semigroup \(\Omega\), such that for any \(\alpha,\beta\in \Omega\), the following axiom is satisfied: \[ R_\alpha(x)R_\beta(y)=R_{\alpha\beta}(R_\alpha(x)y+xR_\beta(y)+\lambda ab), \] where \(\lambda\) is a scalar. This paper generalizes Guo's construction of free Rota-Baxter algebras based on planar leaf-spaced rooted forests. This generalization used planar leaf-spaces rooted trees which leaves are decorated by the generators and edges are typed (or decorated) by elements of \(\Omega\), with constraints on the types. The Rota-Baxter operators just add a root (and a typed edge) and the product is inductively defined using the family Rota-Baxter axiom.
Mathematics Subject Classification ID: 17B38
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16T30
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 7435542
zbMATH Keywords: Rota-Baxter algebras
zbMATH Keywords: Rota-Baxter family algebras
zbMATH Keywords: typed decorated rooted forests
zbMATH Keywords: leaf-spaced
zbMATH Keywords: parallelly typed leaf-spaced decorated
reviewed by: Loïc Foissy
MaRDI profile type: Publication
full work available at URL: math-2020-0059
OpenAlex ID: W3099409637
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DOI: 10.1515/MATH-2020-0059
description: scientific article; zbMATH DE number 7435542