128
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On structure and TKK algebras for Jordan superalgebras

&
Pages 684-704 | Received 27 Oct 2016, Published online: 15 Jun 2017

References

  • Alekseevsky, D., Michor, P., Ruppert, W. (2005). Extensions of super Lie algebras. J. Lie Theory 15(1):125–134.
  • Boelaert, L., De Medts, T., Stavrova, A. Moufang sets and structurable division algebras. To appear in Memoirs of the AMS. ArXiv:1603.00780.
  • Cantarini, N., Kac, V. G. (2007). Classification of linearly compact simple Jordan and generalized Poisson superalgebras. J. Algebra 313(1):100–124.
  • Cheng, S. J., Wang, W. (2012). Dualities and Representations of Lie Superalgebras. Graduate Studies in Mathematics. Vol. 144. Providence, RI: American Mathematical Society.
  • García, E., Neher, E. (2003). Tits-Kantor-Koecher superalgebras of Jordan superpairs covered by grids. Commun. Algebra 31(7):3335–3375.
  • Jacobson, N. (1976). Structure groups and Lie algebras of Jordan algebras of symmetric elements of associative algebras with involution. Adv. Math. 20(2):106–150.
  • Kac, V. G. (1977). Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras. Commun. Algebra 5(13):1375–1400.
  • Kac, V. G. (1977). Lie superalgebras. Adv. Math. 26(1):8–96.
  • Kac, V. G., Martinez, C., Zelmanov, E. (2001). Graded simple Jordan superalgebras of growth one. Mem. Am. Math. Soc. 150(711):140 pp.
  • Kantor, I. L. (1966). Transitive differential groups and invariant connections in homogeneous spaces. Trudy Sem. Vektor. Tenzor. Anal. 13:310–398.
  • Kantor, I. L. (1992). Jordan and Lie Superalgebras Determined by a Poisson Algebra. American Mathematical Society Translations Series 2, Vol. 151. Providence, RI: American Mathematical Society.
  • Kashuba, I., Martin, M. E. (2016). The variety of three-dimensional real Jordan algebras. J. Algebra Appl. 15(8):1650158.
  • Kashuba, I., Serganova, V. (2017). On the Tits–Kantor–Koecher construction of unital Jordan bimodules. J. Algebra 481:420–463.
  • Koecher, M. (1967). Imbedding of Jordan algebras into Lie algebras. I. Am. J. Math. 89:787–816.
  • Krutelevich, S. V. (1997). Simple Jordan superpairs. Commun. Algebra 25(8):2635–2657.
  • Loos, O. (1975). Jordan Pairs. Lecture Notes in Mathematics. Vol. 460. Berlin-New York: Springer-Verlag.
  • Martinez, C., Zelmanov, E. (2010). Representation theory of Jordan superalgebras I. Trans. AMS 362(2):815–846.
  • McCrimmon, K. (2004). A Taste of Jordan Algebras. Universitext. New York: Springer-Verlag.
  • Scheunert, M. (1979). The Theory of Lie Superalgebras. An Introduction. Vol. 716. Lecture Notes in Mathematics. Berlin: Springer.
  • Shtern, A. S. (1995). Representations of finite dimensional Jordan superalgebras of Poisson bracket. Commun. Algebra 23(5):1815–1823.
  • Springer, T. (1973). Jordan Algebras and Algebraic Groups. Vol. 75. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band. New York-Heidelberg: Springer-Verlag.
  • Tits, J. (1962). Une classe d’algèbres de Lie en relation avec les algèbres de Jordan. Nederl. Akad. Wetensch. Proc. Ser. A 65  =  Indag. Math. 24:530–535.

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.