Cyclic homology for Hom-associative algebras

Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan

doi:10.1016/j.geomphys.2015.07.026

Cited by 24 publications

(13 citation statements)

References 31 publications

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“…It will be nice to investigate the properties of a calculus structure on the Hochschild type (co)homology theory of hom-associative algebras. This will be some development on the noncommutative geometry of hom-associative algebras recently initiated in [7].…”

Section: 4mentioning

confidence: 99%

Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Das

2020

Proc Math Sci

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A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-associative algebra. We show that the cup product together with the degree −1 graded Lie bracket (which controls the deformation of the hom-associative algebra structure) on the cohomology forms a Gerstenhaber algebra. This generalizes a classical fact that the Hochschild cohomology of an associative algebra carries a Gerstenhaber algebra structure.2010 Mathematics Subject Classification. 16E40, 17A30.

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Section: 4mentioning

confidence: 99%

Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Das

2020

Proc Math Sci

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“…In [15] the authors consider a definition of Hochschild homology for hom-associative algebras. In the case of bihom-associative algebras, the situation is not that much transparent due to the presence of two commuting maps.…”

Section: Discussionmentioning

confidence: 99%

Cohomology of BiHom-associative algebras

Das¹

2019

Preprint

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Bihom-associative algebras have been recently introduced in the study of group homcategories. In this paper, we introduce a Hochschild type cohomology for bihom-associative algebras with suitable coefficients. The underlying cochain complex (with coefficients in itself) can be given the structure of an operad with a multiplication. Hence, the cohomology inherits a Gerstenhaber structure. We show that this cohomology also control corresponding formal deformations.Finally, we introduce bihom-associative algebras up to homotopy and show that some particular classes of these homotopy algebras are related to the above Hochschild cohomology.

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“…We will use in this article a definition of bimodule of a commutative Hom-associative algebras including Hom-module map condition (2.7), while we note that there are also other definitions of Hom-modules and Hom-bimodules of Hom-associative algebras, for example the more general notions requiring only (2.6), [8,9,39,70,72,95,98]. Definition 2.9.…”

Section: Transposed Hom-poisson Algebrasmentioning

confidence: 99%

Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras

Laraiedh,

Silvestrov

2021

Preprint

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The notions of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras are introduced. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. The notion of Manin triple of transposed Hom-Poisson algebras is introduced, and its equivalence to the transposed Hom-Poisson bialgebras is investigated. The notion of O-operator is exploited to illustrate the relations existing between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.

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Cyclic homology for Hom-associative algebras

Cited by 24 publications

References 31 publications

Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Gerstenhaber algebra structure on the cohomology of a hom-associative algebra

Cohomology of BiHom-associative algebras

Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras and bialgebras

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