Derivations of BiHom-Jacobi-Jordan Superalgebras and BJJYB Equations
Keywords:
Derivations of BiHom-Jacobi; Jordan Superalgebras; BJJYB Equations.Abstract
This paper explores the derivations of BiHom-Jacobi-Jordan algebras, building on classical structures with BiHom-perations and investigating their algebraic properties. We extend this analysis to BiHom-Jacobi-Jordan superalgebras, focusing on the derivations and the complexities introduced by their graded structure. Furthermore, we construct solutions to the BiHom-Jacobi-Jordan Yang-Baxter Equation (BJJYBE) within the context of BiHom-Jacobi-Jordan superalgebras.
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[1] H. Ataguema, A. Makhlouf, and S. Silvestrov, “Generalization of n-ary Nambu algebras and beyond,” Journal of Mathematical Physics 50 (2009), 121702. 1
[2] C. Bai, O. Bellier, L. Guo, and X. Ni, “Splitting of operations, Manin products, and Rota-Baxter operators on Lie algebras,” Communications in Mathematical Physics 290 (2010), 603–634. 1
[3] I. Basdouri, S. Benabdelhafidh, S. Ncib, and M. A. Sadraoui, “Cohomologies of modified Rota-Baxter Lie algebras with derivations and applications,” Advanced Studies: Euro-Tbilisi Mathematical Journal 18(2) (2025), 189–210. 1
[4] I. Basdouri, S. Benabdelhafidh, A. Saghrouni, and S. Silvestrov, “Cohomology and deformations of crossed homomorphisms on Lie conformal algebras,” Advanced Studies: Euro-Tbilisi Mathematical Journal 18(3) (2025), 91–107. 1
[5] I. Basdouri, S. Ghribi, and M. A. Sadraoui, “Maurer-Cartan characterization and cohomology of compatible LieDer and AssDer pairs,” Advanced Studies: Euro-Tbilisi Mathematical Journal 18(3) (2025), 173–205. 1
[6] I. Basdouri, B. Mosbahi, and A. Zahari, “Classification, derivations and centroids of low-dimensional associative trialgebras,” Galois Journal of Algebra 1(1) (2025), 118–136. 1
[7] I. Basdouri, E. Peyghan, M. A. Sadraoui, and R. Saha, “Formal deformations and extensions of twisted Lie algebras,” Advanced Studies: Euro-Tbilisi Mathematical Journal 18(3) (2025), 225–239. 1
[8] G. Benkart and T. Roby, “Down-up algebras,” Journal of Algebra 209(1) (1998), 305–344. 1
[9] G. D. Birkhoff and J. von Neumann, “The logic of quantum mechanics,” Annals of Mathematics 37 (1936), 823–843. 1
[10] C. Chevalley, The Theory of Lie Groups, Princeton University Press, 1946. 1
[11] V. T. Filippov, “n-Lie algebras,” Siberian Mathematical Journal 26 (1985), 879–887. 1
[12] J. Hartwig, D. Larsson, and S. D. Silvestrov, “Deformations of Lie algebras using σ-derivations,” Journal of Algebra 295(2) (2006), 314–361. 1
[13] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, American Mathematical Society, 2001. 1
[14] N. Jacobson, Structure and Representations of Jordan Algebras, American Mathematical Society, 1968. 1
[15] P. Jordan, J. von Neumann, and E. Wigner, “On an algebraic generalization of the quantum mechanical formalism,” Annals of Mathematics 35 (1934), 29–64. 1
[16] A. Makhlouf and S. Silvestrov, “Hom-algebras and Hom-coalgebras,” Journal of Generalized Lie Theory and Applications 3 (2009), 1–22. 1
[17] A. N. Parshin, “On the Yang-Baxter equation,” Communications in Mathematical Physics 128 (1989), 599–607. 1
[18] E. K. Sklyanin, “Quantum inverse scattering method,” Funktsional’nyi Analiz i Prilozheniya 16 (1982), 27–34. 1
[19] T. Zhang and Y. Ma, “BiHom-Lie superalgebra structures on Hom-superalgebras,” Journal of Mathematical Physics 56 (2015), 101703. 1
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Copyright (c) 2026 Ahmed Dhahri, Rim Messaoud
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