On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras
In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2021-11-01
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| Series: | Discussiones Mathematicae - General Algebra and Applications |
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| Online Access: | https://doi.org/10.7151/dmgaa.1361 |
| _version_ | 1797759774279860224 |
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| author | Attan Sylvain Gaparayi Donatien Issa A. Nourou |
| author_facet | Attan Sylvain Gaparayi Donatien Issa A. Nourou |
| author_sort | Attan Sylvain |
| collection | DOAJ |
| description | In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom-Leibniz superalgebra, it is observed that the Hom-super Akivis identity leads to an additional property of Hom-Leibniz superalgebras, which in turn gives a necessary and sufficient condition for Hom-super Lie admissibility of Hom-Leibniz superalgebras. We also show that every (left) Hom-Leibniz superalgebra has a natural super Hom-Lie-Yamaguti structure. |
| first_indexed | 2024-03-12T18:49:17Z |
| format | Article |
| id | doaj.art-18b14fe9f0f54d37b295692d7ce5cda9 |
| institution | Directory Open Access Journal |
| issn | 2084-0373 |
| language | English |
| last_indexed | 2024-03-12T18:49:17Z |
| publishDate | 2021-11-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae - General Algebra and Applications |
| spelling | doaj.art-18b14fe9f0f54d37b295692d7ce5cda92023-08-02T07:18:31ZengUniversity of Zielona GóraDiscussiones Mathematicae - General Algebra and Applications2084-03732021-11-0141224926410.7151/dmgaa.1361On Hom-Leibniz and Hom-Lie-Yamaguti SuperalgebrasAttan Sylvain0Gaparayi Donatien1Issa A. Nourou2Département de Mathématiques, Université d’Abomey-calavi, 01 BP 4521, Cotonou 01, BéninEcole Normale Supérieure (E.N.S), BP 6983 Bujumbura, BurundiDépartement de Mathématiques, Université d’Abomey-calavi, 01 BP 4521, Cotonou 01, BéninIn this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom-Leibniz superalgebra, it is observed that the Hom-super Akivis identity leads to an additional property of Hom-Leibniz superalgebras, which in turn gives a necessary and sufficient condition for Hom-super Lie admissibility of Hom-Leibniz superalgebras. We also show that every (left) Hom-Leibniz superalgebra has a natural super Hom-Lie-Yamaguti structure.https://doi.org/10.7151/dmgaa.1361hom-leibniz superalgebrashom-akivis superalgebrashom-lie-yamaguti superalgebras17a3017a3217d99 |
| spellingShingle | Attan Sylvain Gaparayi Donatien Issa A. Nourou On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras Discussiones Mathematicae - General Algebra and Applications hom-leibniz superalgebras hom-akivis superalgebras hom-lie-yamaguti superalgebras 17a30 17a32 17d99 |
| title | On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras |
| title_full | On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras |
| title_fullStr | On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras |
| title_full_unstemmed | On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras |
| title_short | On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras |
| title_sort | on hom leibniz and hom lie yamaguti superalgebras |
| topic | hom-leibniz superalgebras hom-akivis superalgebras hom-lie-yamaguti superalgebras 17a30 17a32 17d99 |
| url | https://doi.org/10.7151/dmgaa.1361 |
| work_keys_str_mv | AT attansylvain onhomleibnizandhomlieyamagutisuperalgebras AT gaparayidonatien onhomleibnizandhomlieyamagutisuperalgebras AT issaanourou onhomleibnizandhomlieyamagutisuperalgebras |