KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 2

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

Ismail Laraiedh(Sfax University)0000-0003-2966-9974
Sergei Silvestrov(Malardalen University)0000-0003-4554-6528
Sayfa
—
Yayın Tarihi
2026-04-29
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, the notion of $\mathcal{O}$-operator is exploited to establish the relations between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The purpose of this paper is to introduce and give some constructions results and examples of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.
📊
Temel Bulgular & Veri:Also, we establish the bimodules and matched pairs of transposed Hom-Poisson algebras.
💡
Sonuç & Katkı:Finally, the notion of $\mathcal{O}$-operator is exploited to establish the relations between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:transposed Hom-Poisson algebra · Hom-pre-LiePoisson algebra · bimodule

Abstract

The purpose of this paper is to introduce and give some constructions results and examples of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras. Also, we establish the bimodules and matched pairs of transposed Hom-Poisson algebras. Their related relevant properties are also given. Finally, the notion of $\mathcal{O}$-operator is exploited to establish the relations between transposed Hom-Poisson and Hom-pre-Lie Poisson algebras.

🔖

Bu Makaleye Atıf Yap

Laraiedh, I., Silvestrov, S. (2026). Transposed Hom-Poisson and Hom-pre-Lie Poisson algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1417353

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (37)

  1. E. Abdaoui, S. Mabrouk and A. Makhlouf, Rota-Baxter Operators on Pre-Lie Superalgebras, Bull. Malays. Math. Sci. Soc. 42, 1567-1606, 2019.
  2. A. Agore and G. Militaru, Jacobi and Poisson algebras, J. Noncomm. Geom. 9, 1295- 1342, 2015.
  3. C. Bai, R. Bai, L. Guo and Y. Wu, Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras, J. Algebra 632, 535-566, 2023.
  4. A. A. Balinskii and S. P. Novikov, Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras, Soviet Math. Dokl. 32, 228-231, 1985.
  5. P. Beites, B. L. M. Ferreira and I. Kaygorodov, Transposed Poisson Structures, Results Math 79, 93, 2024.
  6. L. Bokut, Y. Chen and Z. Zhang, On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem, J. Algebra 500, 153-170, 2016.
  7. T. Chtioui, S. Mabrouk and A. Makhlouf, Cohomology and deformations of $\mathcal{O}$-operators on Hom-associative algebras, J. Algebra 604, 727-759, 2022.
  8. B.L.M. Ferreira, I. Kaygorodov and V. Lopatkin, $\frac{1}{2}$ -derivations of Lie algebras and transposed Poisson algebras, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115, 142, 2021.
  9. I.M. Gel’fand and I. Ya. Dorfman, Hamiltonian operators and algebraic structures related to them, Funct. Anal. Appl. 13, 248-262, 1979.
  10. J. Grabowski and G. Marmo, Remarks on Nambu-Poisson and Nambu-Jacobi bracket, J. Phys. A: Math. Gen. 32, 4239-4247, 1999.
  11. J.T. Hartwig, D. Larsson and S.D. Silvestrov, Deformations of Lie algebras using $\sigma$-derivations, J. Algebra 295, 314-361, 2006.
  12. M.N. Hounkonnou, G.D. Houndedji and S. Silvestrov, Double Constructions of BiHom-Frobenius Algebras, in: S. Silvestrov, A. Malyarenko (eds.), Non-commutative and Non-associative Algebra and Analysis Structures. SPAS 2019, Springer Proceedings in Mathematics and Statistics 426, Springer, Cham, Ch. 18, 477-523, 2023.
  13. J. Huebschmann, Poisson cohomology and quantization, J. Reine Angew. Math. 408, 57-113, 1990.
  14. M. Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66, 157-216, 2003.
  15. Y. Kosmann-Schwarzbach, From Poisson to Gerstenhaber algebras, Ann. Inst. Fourier 46, 1243-1274, 1996.
  16. I. Laraiedh, Bimodules and matched pairs of noncommutative BiHom-(pre)-Poisson algebras, Hacet. J. Math. Stat. 52, 673-697, 2023.
  17. D. Larsson, G. Sigurdsson and S.D. Silvestrov, Quasi-Lie deformations on the algebra $\mathbb{F}[t]/(t^N)$, J. Gen. Lie Theory Appl. 2 (3), 201-205, 2008.
  18. D. Larsson and S.D. Silvestrov, Quasi-Hom-Lie algebras, central extensions and 2- cocycle-like identities, J. Algebra 288, 321-344, 2005.
  19. D. Larsson and S.D. Silvestrov, Quasi-Lie algebras, in: J. Fuchs, J. Mickelsson, G. Rozenblioum, A. Stolin, A. Westerberg (eds.), Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemp. Math. 391, Amer. Math. Soc., Providence, RI, 241-248, 2005.
  20. L. Li, Classical r-matrices and compatible Poisson structures for Lax equations on Poisson algebras, Comm. Math. Phys. 203, 573-592, 1999.
  21. A. Lichnerowicz, Les variétiés de Poisson et leurs algèbras de Lie associées, J. Diff. Geom. 12, 253-300, 1977.
  22. T. Ma, A. Makhlouf and S. Silvestrov, Rota-Baxter Cosystems and Coquasitriangular Mixed Bialgebras, J. Algebra Appl. 20 (04), 2150064, 2021.
  23. S. Mabrouk, O. Ncib and S. Silvestrov, Generalized Derivations and Rota-Baxter Operators of n-ary Hom-Nambu Superalgebras, Adv. Appl. Clifford Algebras 31, 32, 2021.
  24. A. Makhlouf, Hom-dendriform algebras and Rota-Baxter Hom-algebras, in: C. Bai, L. Guo, J.-L. Loday, (eds.), Nankai Ser. Pure Appl. Math. Theoret. Phys. 9, World Sci. Publ. 147-171, 2012.
  25. A. Makhlouf and S.D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl. 2 (2), 51-64, 2008.
  26. A. Makhlouf and S. Silvestrov, Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras, in: S. Silvestrov, E. Paal, V. Abramov, A. Stolin (eds.), Generalized Lie Theory in Mathematics, Physics and Beyond, Springer-Verlag, Berlin, Heidelberg, Ch. 17, 189-206, 2009.
  27. A. Makhlouf and S. Silvestrov, Notes on 1-parameter formal deformations of Homassociative and Hom-Lie algebras, Forum Math. 22 (4), 715-739, 2010.
  28. G. Rinehart, Differential forms for general commutative algebras, Trans. Amer. Math. Soc. 108, 195-222, 1963.
  29. Y. Sheng, Representations of Hom-Lie algebras, Algebr. Reprensent. Theory 15, 1081- 1098, 2012.
  30. Y. Sheng and C. Bai, A new approach to Hom-Lie bialgebras, J. Algebra 399, 232-250, 2014.
  31. Q. Sun and H. Li, On parakähler hom-Lie algebras and hom-left-symmetric bialgebras, Comm. Algebra 45 (1), 105-120, 2017.
  32. P. Xu, Noncommutative Poisson algebras, Amer. J. Math. 116, 101-125, 1994.
  33. X. Xu, Novikov-Poisson algebras, J. Algebra 190, 253-279, 1997.
  34. D. Yau, Hom-algebras and homology, J. Lie Theory 19 (2), 409-421, 2009.
  35. D. Yau, Non-commutative hom-Poisson algebras, arXiv: 1010.3408 [math.QA].
  36. D. Yau, Hom-Malcev, Hom-alternative, and Hom-Jordan algebras, Int. Electron. J. Algebra 11, 177-217, 2012.
  37. D. Yau, Non-commutative hom-Poisson algebras, arXiv: 1010.3408 [math.QA].