On Hom-Jacobi algebra structures

Document Type : Research Paper

Authors

1 Facult\'e des Sciences et Techniques‎, ‎Universit\'e Marien Ngouabi‎‎‎, ‎Brazzaville‎, ‎Congo

2 Ecole Normale Sup\'erieure‎, ‎Universit\'e Marien Ngouabi‎‎‎, ‎Brazzaville‎, ‎Congo‎

Abstract

We define hom-Jacobi algebras as an extension of hom-Poisson algebras and we give some examples. We describe the universal property of first-order hom-differential operators as well as the universal property of first-order hom-differential multi-operators. By using these universal properties, we prove the existence and uniqueness of a canonical purely hom-Jacobi form associated to purely hom-Jacobi algebra.

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References

[1] A. L. Agore and G. Militaru, Jacobi and Poisson algebras, J. Noncommut. Geom., 9 (2015),1295-1342.
[2] J. Casas, M. Insua and N. Pacheco, On universal central extensions of Hom-Lie algebras, Hacet. J. Math. Stat., (2) 44 (2015), 277-288.
[3] J. Grabowski and G. Marmo, Jacobi structures revisited, J. Phys. A: Math. Gen., 34 (2001), 10975-10990.
[4] J. Grabowski and G. Marmo, The graded Jacobi algebras and (co)homology, J. Phys. A, 36 (2003), 161-181.
[5] J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra, 295 (2006), 314-361.
[6] A. Kirillov, Local Lie algebras, Russ. Math. Surv., 31 (1976), 55-75.
[7] C. Laurent-Gengoux and J. Teles, Hom-Lie algebroids, J. Geom. Phys., 68 (2013), 69-75.
[8] C. Laurent-Gengoux, A. Pichereau and P. Vanhaecke, Poisson Structures, 347 (2013), Springer.
[9] A. Lichnerowicz, Les variétés de Jacobi et leurs algèbres de Lie associées, J. Math. Pures Appl., (57) 9 (1978), 453-488.
[10] A. Makhlouf and S. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2008), 51-64.
[11] A. Makhlouf and S. Silvestrov, Notes on 1-parameter formal deformations of Homassociative and Hom-Lie algebras, Forum Math., (22) 4 (2010), 715-759.
[12] A. Mandal and S. K. Mishra, Hom-Lie-Rinehart algebras, Commun. Algebra, (46) 9 (2016), 3722-3744.
[13] E. Okassa, On Lie-Rinehart-Jacobi algebras, J. Algebra Appl., (7) 6 (2008), 749-772.
Journal of Algebra and Related Topics
Volume 14, Issue 1
August 2026
Pages 49-68

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