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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8540674 |
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| _version_ | 1832560119821369344 |
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| author | Liangyun Zhang Linhan Li Huihui Zheng |
| author_facet | Liangyun Zhang Linhan Li Huihui Zheng |
| author_sort | Liangyun Zhang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-7d441ce97ee8492d948aa8a4dd2170c3 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-7d441ce97ee8492d948aa8a4dd2170c32025-02-03T01:28:26ZengWileyAdvances 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 |
| spellingShingle | Liangyun Zhang Linhan Li Huihui Zheng Rota-Baxter Leibniz Algebras and Their Constructions Advances in Mathematical Physics |
| title | 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_short | Rota-Baxter Leibniz Algebras and Their Constructions |
| title_sort | rota baxter leibniz algebras and their constructions |
| url | http://dx.doi.org/10.1155/2018/8540674 |
| work_keys_str_mv | AT liangyunzhang rotabaxterleibnizalgebrasandtheirconstructions AT linhanli rotabaxterleibnizalgebrasandtheirconstructions AT huihuizheng rotabaxterleibnizalgebrasandtheirconstructions |