Abstract
In this paper, the super 
-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super 
-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super 
-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albert A A. On Jordan algebras of linear transformations. Trans Amer Math Soc, 1946, 59: 524–555
Albert A A. A structure theory for Jordan algebras. Ann Math, 1946, 48: 546–567
Iordanescu R. Jordan Structures in Geometry and Physics. Bucarest: Editura Acad Romane, 2003
Chu C H. Jordan triple systems and Riemannian symmetric spaces. Adv Math, 2008, 219: 2029–2057
Chu C H. Jordan Structures in Geometry and Analysis. Cambridge: Cambridge University Press, 2012
Hou D P, Ni X, Bai C M. Pre-Jordan algebras. Math Scand, 2013, 112(1): 19–48
Jacobson N. Lie and Jordan triple systems. Amer J Math, 1949, 71: 149–170
Jordan P, von Neumann J, Winger E P. On an algebraic generalization of the quantum mechanical formalism. Ann Math, 1934, 35: 29–64
Kac V. Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras. Comm Algebra, 1977, 5: 1375–1400
Kantor I L. Connection between Poisson brackets and Jordan and Lie superalgebras. In: Lie Theory, Differential Equations and Representation Theory (Montreal, PQ, 1989). 1990, 213–225
Kantor I L. Jordan and Lie superalgebras defined by Poisson brackets. In: Algebra and Analysis (Tomsk), 1989, 51–80; Amer Math Soc Transl, Ser 2, 1992, 151: 55–80
Kaplansky I. Superalgebras. Pacific J Math, 1980, 86: 93–98
Kaup W, Zaitsev D. On symmetric Cauchy-Riemann manifolds. Adv Math, 2000, 149: 145–181
Koecher M. Imbedding of Jordan algebras into Lie algebras I. Amer J Math, 1967, 89: 787–816
Racine M, Zelmanov E. Simple Jordan superalgebras with semisimple even part. J Algebra, 2003, 270(2): 374–444
Upmeier H. Jordan algebras and harmonic analysis on symmetric spaces. Amer J Math, 1986, 108: 1–25
Zhelyabin V N. Jordan bialgebras and their relation to Lie bialgebras. Algebra Logic, 1997, 36: 1–15
Zhelyabin V N. On a class of Jordan D-bialgebras. St Petersburg Math J, 2000, 11: 589–610
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ni, J., Wang, Y. & Hou, D. Super 
-operators of Jordan superalgebras and super Jordan Yang-Baxter equations.
Front. Math. China 9, 585–599 (2014). https://doi.org/10.1007/s11464-014-0339-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11464-014-0339-9
-operator