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Journals / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 4

On Hom-F-manifold algebras and quantization

Abdelkader BEN HASSINE
Taoufik CHTIOUI
Sami MABROUK
Mohamed Ali MAALAOUI
Pages
1153–1176
Publication Date
2022-11-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we study Hom-Lie infinitesimal deformations and extension of Hom-pre-Lie n-deformation to Hom-preLie (n + 1)-deformation of a commutative Hom-associative algebra via cohomology theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The notion of a F -manifold algebras is an algebraic description of a F -manifold.
📊
Key Findings & Data:In this paper, we introduce the notion of Hom-F -manifold algebras which is generalisation of F -manifold algebras and Hom-Poisson algebras.
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Conclusion & Impact:Finally, we study Hom-Lie infinitesimal deformations and extension of Hom-pre-Lie n-deformation to Hom-preLie (n + 1)-deformation of a commutative Hom-associative algebra via cohomology theory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The notion of a F -manifold algebras is an algebraic description of a F -manifold. In this paper, we introduce the notion of Hom-F -manifold algebras which is generalisation of F -manifold algebras and Hom-Poisson algebras. We develop the representation theory of Hom-F -manifold algebras and generalize the notion of Hom-pre-Poisson algebras by introducing the Hom-pre-F -manifold algebras which give rise to a Hom-F -manifold algebra through the subadjacent commutative Hom-associative algebra and the subadjacent Hom-Lie algebra. Using O -operators on a Hom-F -manifold algebras we construct a Hom-pre-F -manifold algebras on a module. Then, we study Hom-pre-Lie formal deformations of commutative Hom-associative algebra and we prove that Hom-F -manifold algebras are the corresponding semiclassical limits. Finally, we study Hom-Lie infinitesimal deformations and extension of Hom-pre-Lie n-deformation to Hom-preLie (n + 1)-deformation of a commutative Hom-associative algebra via cohomology theory.

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Cite This Article

HASSINE, A. B., CHTIOUI, T., MABROUK, S., MAALAOUI, M. A. (2022). On Hom-F-manifold algebras and quantization. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 4, 1153–1176. https://ajindex.com/articles/605111

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