Construction of Hom-pre-Jordan algebras and Hom-J-dendriform algebras

• T. Chtioui ^[1] ; S. Mabrouk ^[2] ; A. Makhlouf ^[3]
  1. [1] University of Sfax

     University of Sfax

     Túnez

     
  2. [2] University of Gafsa

     University of Gafsa

     Túnez

     
  3. [3] Université de Haute Alsace, IRIMAS - Département de Mathématiques F-68093 Mulhouse, France

  Mostrar afiliaciones +
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 1, 2023, págs. 27-50
• Idioma: inglés
• DOI: 10.17398/2605-5686.38.1.27
• Enlaces
  • Texto completo
• Resumen

  • The aim of this work is to introduce and study the notions of Hom-pre-Jordan algebra and Hom-J-dendriform algebra which generalize Hom-Jordan algebras. Hom-pre-Jordan algebras are regarded as the underlying algebraic structures of the Hom-Jordan algebras behind the Rota-Baxter operators and O-operators introduced in this paper. Hom-pre-Jordan algebras are also analogues of Hom-pre-Lie algebras for Hom-Jordan algebras. The anti-commutator of a Hom-pre-Jordan algebra is a Hom-Jordan algebra and the left multiplication operator gives a representation of a Hom-Jordan algebra. On the other hand, a Hom-J-dendriform algebra is a Hom-Jordan algebraic analogue of a Hom-dendriform algebra such that the anti-commutator of the sum of the two operations is a Hom-pre-Jordan algebra.

• Referencias bibliográficas
  • M. Aguiar, J.-L. Loday, Quadri-algebras, J. Pure Appl. Algebra 191 (2004), 205 – 221.
  • C. Bai, O. Bellier, L. Guo, X. Ni, Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN 2013 (3)...
  • C.-H. Chu, Jordan triples and Riemannian symmetric spaces, Adv. Math. 219 (2008), 2029 – 2057.
  • J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, J. Algebra 295 (2006), 314 – 361.
  • D. Hou, C. Bai, J-dendriform algebras, Front. Math. China 7 (2012) (1), 29 – 49.
  • D. Hou, X. Ni, C. Bai, Pre-Jordan algebras, Math. Scand. 112 (1) (2013), 19 – 48.
  • N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. 71 (1949), 149 – 170.
  • J.-L. Loday, M. Ronco, Trialgebras and families of polytopes, in “ Homotopy Theory: relations with Algebraic Geometry, Group Cohomology, and...
  • J.-L. Loday, “ Dialgebras ”, Lecture Notes in Math. 1763, Springer, Berlin, 2001, 7 – 66.
  • A. Makhlouf, Hom-dendriform algebras and Rota-Baxter Hom-algebras, in “ Operads And Universal Algebra ”, Nankai Ser. Pure Appl. Math. Theoret....
  • A. Makhlouf, Hom-alternative algebras and Hom-Jordan algebras, Int. Electron. J. Algebra 8 (2010), 177 – 190.
  • Q. Sun, On Hom-prealternative bialgebras, Algebr. Represent. Theory 19 (3) (2016), 657 – 677.
  • Y. Sun, Z. Huang, S. Zhao, Z. Tian, Classification of pre-Jordan Algebras and Rota-Baxter Operators on Jordan Algebras in Low Dimensions,...
  • H. Upmeier, Jordan algebras and harmonic analysis on symmetric spaces, Amer. J. Math. 108 (1986), 1 – 25.
  • D. Yau, Hom-Maltsev, Hom-alternative and Hom-Jordan algebras, Int. Electron. J. Algebra 11 (2012), 177 – 217.