The main goal of this paper is to introduce the notion of 3-L-dendriform
algebras which are the dendriform version of 3-pre-Lie algebras. In fact
they are the algebraic structures behind the ...O-operator of 3-pre-Lie
algebras. They can be also regarded as the ternary analogous of L-dendriform
algebras. Moreover, we study the generalized derivations of 3-L-dendriform
algebras. Finally, we explore the spaces of quasi-derivations, the centroids
and the quasi-centroids and give some properties.
In this paper, we define and study (co)homology theories of a compatible associative algebra. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible ...associative structures on a vector space. Then we define the cohomology of a compatible associative algebra A and as applications, we study extensions, deformations and extensibility of finite order deformations of A. We end this paper by considering compatible presimplicial vector spaces and the homology of compatible associative algebras.
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In this paper, we introduce the cohomology theory of O-operators on Hom-associative algebras. This cohomology can also be viewed as the Hochschild cohomology of a certain Hom-associative algebra with ...coefficients in a suitable bimodule. Next, we study infinitesimal and formal deformations of an O-operator and show that they are governed by the above-defined cohomology. Furthermore, the notion of Nijenhuis elements associated with an O-operator is introduced to characterize trivial infinitesimal deformations. Moreover, we provide relevant constructions that twists objects on associative algebras to objects on Hom-associative algebras along morphisms.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The purpose of this paper is to introduce and study BiHom-alternative algebras and BiHom-Malcev algebras. It is shown that BiHom-alternative algebras are BiHom-Malcev admissible and BiHom-Jordan ...admissible. Moreover, BiHom-type generalizations of some well known identities in alternative algebras, including the Moufang identities, are obtained.
The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative ...linear maps. We study cohomology and one-parameter formal deformation theory of left BiHom-alternative algebras. Moreover, we study central and $T_\theta$-extensions of BiHom-alternative algebras and their relationship with cohomology. Finally, we investigate generalized derivations and give some relevant results.
The purpose of this paper is to introduce and study the notion of BiHom-pre-alternative algebra which may be viewed as a BiHom-alternative algebra whose product can be decomposed into two compatible ...pieces. Furthermore, we introduce the notion of BiHom-alternative quadri-algebra and show the connections between all these algebraic structures using Rota-Baxter operators and 𝒪-operators.
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The goal of this work is to introduce the notion of 3-Hom-L-dendriform algebras which is the dendriform version of 3-Hom-Lie-algebras. They can be also regarded as the ternary analogous of ...Hom-L-dendriform algebras. We give the representation of a 3-Hom-pre-Lie algebra. Moreover, we introduce the notion of Nijenhuis operators on a 3-Hom-pre-Lie algebra and provide some constructions of 3-Hom-L-dendriform algebras in term of Nijenhuis operators. Parallelly, we introduce the notion of a product and complex structures on a 3-Hom-L-dendriform algebras and there are also four types special integrability conditions.
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