Associative-Yamaguti algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914020214177792 |
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| author | Das, Apurba |
| author_facet | Das, Apurba |
| contents | In this paper, we first introduce associative-Yamaguti algebras as the associative analogue of Lie-Yamaguti algebras. Associative algebras, reductive associative algebras and associative triple systems of the first kind form subclasses of associative-Yamaguti algebras. Any diassociative algebra canonically provides an associative-Yamaguti algebra structure. We confirm that any associative-Yamaguti algebra admits an enveloping associative algebra (i.e., it can be obtained from a reductive associative algebra). We show that a suitable skew-symmetrization of an associative-Yamaguti algebra gives rise to a Lie-Yamaguti algebra structure. Next, we define the $(2,3)$-cohomology group of an associative-Yamaguti algebra to study formal one-parameter deformations and abelian extensions. Later, we consider Yamaguti multiplications on a nonsymmetric operad as a generalization of associative-Yamaguti algebras. This notion further leads us to introduce dendriform-Yamaguti algebras, which are splitting objects for associative-Yamaguti algebras. Finally, we consider relative Rota-Baxter operators on associative-Yamaguti algebras to establish close relationships with dendriform-Yamaguti algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_03648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associative-Yamaguti algebras Das, Apurba Rings and Algebras Representation Theory 17A30, 17A40, 17B60, 16E99, 17A36 In this paper, we first introduce associative-Yamaguti algebras as the associative analogue of Lie-Yamaguti algebras. Associative algebras, reductive associative algebras and associative triple systems of the first kind form subclasses of associative-Yamaguti algebras. Any diassociative algebra canonically provides an associative-Yamaguti algebra structure. We confirm that any associative-Yamaguti algebra admits an enveloping associative algebra (i.e., it can be obtained from a reductive associative algebra). We show that a suitable skew-symmetrization of an associative-Yamaguti algebra gives rise to a Lie-Yamaguti algebra structure. Next, we define the $(2,3)$-cohomology group of an associative-Yamaguti algebra to study formal one-parameter deformations and abelian extensions. Later, we consider Yamaguti multiplications on a nonsymmetric operad as a generalization of associative-Yamaguti algebras. This notion further leads us to introduce dendriform-Yamaguti algebras, which are splitting objects for associative-Yamaguti algebras. Finally, we consider relative Rota-Baxter operators on associative-Yamaguti algebras to establish close relationships with dendriform-Yamaguti algebras. |
| title | Associative-Yamaguti algebras |
| topic | Rings and Algebras Representation Theory 17A30, 17A40, 17B60, 16E99, 17A36 |
| url | https://arxiv.org/abs/2509.03648 |