Rota-Baxter Leibniz Algebras and Their Constructions

Rota-Baxter Leibniz Algebras and Their Constructions

In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augm...

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Main Authors: Liangyun Zhang, Linhan Li, Huihui Zheng
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/8540674
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spelling doaj-7d441ce97ee8492d948aa8a4dd2170c32021-07-02T12:26:21ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/85406748540674Rota-Baxter Leibniz Algebras and Their ConstructionsLiangyun Zhang0Linhan Li1Huihui Zheng2College of Science, Nanjing Agricultural University, Nanjing, Jiangsu 210095, ChinaCollege of Science, Nanjing Agricultural University, Nanjing, Jiangsu 210095, ChinaCollege of Science, Nanjing Agricultural University, Nanjing, Jiangsu 210095, ChinaIn this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.http://dx.doi.org/10.1155/2018/8540674
collection DOAJ
language English
format Article
sources DOAJ
author Liangyun Zhang
Linhan Li
Huihui Zheng
spellingShingle Liangyun Zhang
Linhan Li
Huihui Zheng
Rota-Baxter Leibniz Algebras and Their Constructions
Advances in Mathematical Physics
author_facet Liangyun Zhang
Linhan Li
Huihui Zheng
author_sort Liangyun Zhang
title Rota-Baxter Leibniz Algebras and Their Constructions
title_short Rota-Baxter Leibniz Algebras and Their Constructions
title_full Rota-Baxter Leibniz Algebras and Their Constructions
title_fullStr Rota-Baxter Leibniz Algebras and Their Constructions
title_full_unstemmed Rota-Baxter Leibniz Algebras and Their Constructions
title_sort rota-baxter leibniz algebras and their constructions
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.
url http://dx.doi.org/10.1155/2018/8540674
work_keys_str_mv AT liangyunzhang rotabaxterleibnizalgebrasandtheirconstructions
AT linhanli rotabaxterleibnizalgebrasandtheirconstructions
AT huihuizheng rotabaxterleibnizalgebrasandtheirconstructions
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