Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

Some characterizations of color Hom-Poisson algebras

Pages
1552–1563
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

This enables us to explore color Hom-Poisson algebras in the realm of non-Hom-associative color algebras.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we describe color Hom-Poisson structures in terms of a single bilinear operation.
📊
Key Findings & Data:In this paper, we describe color Hom-Poisson structures in terms of a single bilinear operation.
💡
Conclusion & Impact:This enables us to explore color Hom-Poisson algebras in the realm of non-Hom-associative color algebras.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Color Hom-Poisson algebras · color Hom-flexible algebras · admissible color Hom-Poisson algebras

Abstract

In this paper, we describe color Hom-Poisson structures in terms of a single bilinear operation. This enables us to explore color Hom-Poisson algebras in the realm of non-Hom-associative color algebras.

🔖

Cite This Article

ATTAN, S. (2022). Some characterizations of color Hom-Poisson algebras. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1552–1563. https://ajindex.com/articles/529871

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Abdaoui, K., Ammar, F., Makhlouf, A. Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras, Bull. Malays. Math. Sci. Soc., 40 (1), 439-472, 2017.
  2. Aizawa, N., Sato, H. q-deformation of the Virasoro algebra with central extension; Phys. Lett. B, 256 (1), 185-190, 1991.
  3. Ammar, F., Makhlouf, A. Hom-Lie and Hom-Lie admissible superalgebras, J. Algebra, 324 (7), 1513-1528, 2010.
  4. Arnold, V. I. Mathematical methods of classical mechanics, Grad. Texts in Math. 60, Springer, Berlin, 1978.
  5. Bakayoko, I. Modules over color Hom-Poisson algebras, J. Gen. Lie Theory Appl., 8 (1) (2014), doi:10.4172/1736-4337.1000212. Chaichian, M., Kulish, P., Lukierski, J. q-Deformed Jacobi identity, q-oscillators and q-deformed infinite-dimensional algebras, Phys. Lett. B., 237 (3)(4), 401-406, 1990.
  6. Chari, V., Pressley, A. N. A guide to quantum groups, Cambridge Univ. Press, Cambridge, 1994.
  7. Curtright, T. L., Zachos, C. K. Deforming maps for quantum algebras, Phys. Lett. B 243 (3), 237-244, 1990.
  8. Drinfel'd, V. G. Quantum groups, in: Proc. ICM (Berkeley, 1986), p.798-820,
  9. AMS, Providence, RI, 1987.
  10. Frenkel, E., Ben-Zvi, D. Vertex algebras and algebraic curves, Math Surveys and Monographs 88, 2nd ed., AMS, Providence, RI, 2004.
  11. Gerstenhaber, M. On the deformation of rings and algebras, Ann. Math., 79, 59-103, 1964.
  12. Goze, M., Remm, E. Poisson algebras in terms of non-associative algebras, J. Algebra, 320 (1), 294-317, 2008.
  13. Hartwig, J. T., Larsson, D. and Silvestrov, S. D. Deformations of Lie algebras using $\sigma-$derivations, J. Algebra, 295 (2), 314-361, 2006.
  14. Hu, N. q-Witt algebras, q-Lie algebras, q-holomorph structure and representations, Algebra Colloq., 6 (1), 51-70, 1999.
  15. Kassel, C. Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Commun. Math. Phys., 146, 343-351, 1992.
  16. Kontsevich, M. Deformation quantization of Poisson manifolds, Lett. Math. Phys., 66, 157-216, 2003.
  17. Makhlouf, A., Silvestrov, S. D. Hom-algebra structures, J. Gen. Lie Theory Appl., 2 (2), 51-64, 2008.
  18. Makhlouf, A., Silvesrov, S. D. Notes on Formal deformations of Hom-Associative and Hom-Lie algebras, Forum Math., 22 (4), 715-759, 2010.
  19. M. Markl, M., E. Remm, E. Algebras with one operation including Poisson and other Lie-admissible algebras, J. Algebra, 299 (1), 171-189, 2006.
  20. J. Nan, J., Wang, C. and Zhang, Q. Hom-Malcev superalgebras, Front. Math. China DOI 10.1007/s11464-014-0351-0.
  21. Schaller, P., Strobl, T. Poisson structure induced (topological) field theories, Mod. Phys.