207
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

On a ternary generalization of Jordan algebras

ORCID Icon, & ORCID Icon
Pages 1074-1102 | Received 21 Oct 2017, Accepted 18 Feb 2018, Published online: 05 Mar 2018

References

  • Jordan P , von Neumann J , Wigner E . On an algebraic generalization of the quantum mechanical formalism. Ann Math Princeton. 1934;35(1):29–64.
  • Schafer RD . Noncommutative Jordan algebras of characteristic 0. Proc Amer Math Soc. 1955;6:472–475.
  • Faraut J , Koranyi A . Analysis on symmetric cones. Oxford mathematical monographs. New York (NY): The Clarendon Press, Oxford University Press; 1994.
  • Upmeier H . Symmetric Banach manifolds and Jordan C\textsuperscript{*} algebras. Vol. 104, North Holland mathematics studies. Elsevier; 1985.
  • Faybusovich L . Jordan-algebraic aspects of optimization: randomization. Optim Methods Softw. 2010;25(5):763–779.
  • McCrimmon K . A taste of Jordan algebras. Berlin, New York (NY): Universitext, Springer-Verlag; 2004.
  • Iordanescu R . Jordan structures in mathematics and physics. 2011, arXiv1106.4415.
  • Bremner M , Hentzel I . Identities for generalized Lie and Jordan products on totally associative triple systems. J Algebra. 2000;231(1):387–405.
  • Gnedbaye AV , Wambst M . Jordan triples and operads. In: Proceedings of Renaissance Conferences. Vol. 202. American Mathematical Society; 2007. p. 83–113.
  • Bremner M . New ternary versions of Jordan algebras. Algebra Colloquium. 2001;8(1):11–24.
  • Osborn JM . Lie triple algebras with one generator. Math Z. 1969;110:52–74.
  • Sidorov AV . Lie triple algebras. Algebra Logic. 1981;87:72–78.
  • Faulkner JR . The inner derivations of a Jordan algebra. Bull Amer Math Soc. 1967;73(2):208–210.
  • Filippov VT . n-Lie algebras. Sib Math J. 1985;26(6):126–140.
  • Hanlon P , Wachs M . On Lie k-algebras. Adv Math. 1995;113(2):206–236.
  • Beites PD , Nicolas AP , Pozhidaev AP , et al . On identities of a ternary quaternion algebra. Commun Algebra. 2011;39(3):830–842.
  • Bremner MR , Peresi LA . Classification of trilinear operations. Commun Algebra. 2007;35(9):2932–2959.
  • Jacobson N . A note on automorphisms and derivations of Lie algebras. Proc Amer Math Soc. 1955;6:281–283.
  • Kaygorodov I , Popov Yu . A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations. J Algebra. 2016;456:323–347.
  • Schafer RD . On the algebras formed by the Cayley--Dickson process. Amer J Math. 1954;76:435–446.
  • Kantor IL . Some generalizations of Jordan algebras. Trudy Sem Vektor Tenzor Anal. 1972;16:407–499.
  • Koecher M . Imbedding of Jordan algebras into Lie algebras I. Amer J Math. 1967;89:787–816.
  • Tits J . Une classe d’algébres de Lie en relation avec les algébres de Jordan. Indag Math. 1962;24:530–534.
  • Pozhidaev AP . n-ary Mal’tsev algebras. Algebra Logic. 2001;40(3):309–329.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.