Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras
The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-opera...
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| Format: | Article |
| Language: | English |
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University of Extremadura
2022-12-01
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| Series: | Extracta Mathematicae |
| Subjects: | |
| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/1801 |
| _version_ | 1811213510850379776 |
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| author | T. Chtioui S. Mabrouk A. Makhlouf |
| author_facet | T. Chtioui S. Mabrouk A. Makhlouf |
| author_sort | T. Chtioui |
| collection | DOAJ |
| description |
The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.
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| first_indexed | 2024-04-12T05:47:50Z |
| format | Article |
| id | doaj.art-93d86152f39849e7beca9db50896cbe4 |
| institution | Directory Open Access Journal |
| issn | 0213-8743 2605-5686 |
| language | English |
| last_indexed | 2024-04-12T05:47:50Z |
| publishDate | 2022-12-01 |
| publisher | University of Extremadura |
| record_format | Article |
| series | Extracta Mathematicae |
| spelling | doaj.art-93d86152f39849e7beca9db50896cbe42022-12-22T03:45:25ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862022-12-01Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebrasT. Chtioui0S. Mabrouk1A. Makhlouf2University of Sfax, Faculty of Sciences Sfax, BP 1171, 3038 Sfax, TunisiaUniversity of Gafsa, Faculty of Sciences Gafsa, 2112 Gafsa, TunisiaUniversité de Haute Alsace, IRIMAS - Département de Mathématiques F-68093 Mulhouse, France The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra. https://publicaciones.unex.es/index.php/EM/article/view/1801Hom-Jordan algebraHom-pre-Jordan algebraHom-J-dendriform algebraO-operator |
| spellingShingle | T. Chtioui S. Mabrouk A. Makhlouf Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras Extracta Mathematicae Hom-Jordan algebra Hom-pre-Jordan algebra Hom-J-dendriform algebra O-operator |
| title | Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras |
| title_full | Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras |
| title_fullStr | Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras |
| title_full_unstemmed | Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras |
| title_short | Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras |
| title_sort | construction of hom pre jordan algebras and hom j dendriform algebras |
| topic | Hom-Jordan algebra Hom-pre-Jordan algebra Hom-J-dendriform algebra O-operator |
| url | https://publicaciones.unex.es/index.php/EM/article/view/1801 |
| work_keys_str_mv | AT tchtioui constructionofhomprejordanalgebrasandhomjdendriformalgebras AT smabrouk constructionofhomprejordanalgebrasandhomjdendriformalgebras AT amakhlouf constructionofhomprejordanalgebrasandhomjdendriformalgebras |