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arXiv · 2509.03648

Associative-Yamaguti algebras

Apurba Das
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Abstract

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.

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Apurba Das. 2025-09-03. Associative-Yamaguti algebras. https://arxiv.org/abs/2509.03648

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