Siberian Mathematical Journal

, Volume 56, Issue 3, pp 411–424 | Cite as

(−1, 1)-Superalgebras of vector type: Jordan superalgebras of vector type and their universal envelopings

  • V. N. ZhelyabinEmail author


We establish a connection between the integral domains, the projective finitely generated modules over them, the derivations of an integral domain and the (−1, 1)-superalgebras of vector type. We study the properties of the universal associative envelopings of the simple Jordan superalgebras of vector type.


Jordan superalgebra (−1, 1)-superalgebra twisted superalgebra of vector type differentiably simple algebra projective module universal envelopings 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kantor I. L., “Jordan and Lie superalgebras determined by a Poisson algebra,” in: Proceedings of the Second Siberian School “Algebra and Analysis” (Tomsk, 1989), Amer. Math. Soc., Providence, 1992, pp. 55–80.Google Scholar
  2. 2.
    King D. and McCrimmon K., “The Kantor construction of Jordan superalgebras,” Comm. Algebra, 20, No. 1, 109–126 (1992).zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    King D. and McCrimmon K., “The Kantor doubling process revisited,” Comm. Algebra, 23, No. 1, 357–372 (1995).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Shestakov I. P., “Simple superalgebras of the kind (−1, 1),” Algebra and Logic, 37, No. 6, 411–422 (1998).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhelyabin V. N., “Simple special Jordan superalgebras with associative nil-semisimple even part,” Algebra and Logic, 41, No. 3, 152–172 (2002).MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zhelyabin V. N. and Shestakov I. P., “Simple special Jordan superalgebras with associative even part,” Siberian Math. J., 45, No. 5, 860–882 (2004).MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zhelyabin V. N., “Differential algebras and simple Jordan superalgebras,” Siberian Adv. Math., 20, No. 3, 223–230 (2010).CrossRefGoogle Scholar
  8. 8.
    Zhelyabin V. N., “New examples of simple Jordan superalgebras over an arbitrary field of characteristic 0,” St. Petersburg Math. J., 24, No. 4, 591–600 (2013).zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Cantarini N. and Kac V. G., “Classification of linearly compact simple Jordan and generalized Poisson superalgebras,” J. Algebra, 313, No. 2, 100–124 (2007).zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Zhelyabin V. N., “Examples of prime Jordan superalgebras of vector type and superalgebras of Cheng-Kac type,” Siberian Math. J., 54, No. 1, 33–39 (2013).zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Zhelyabin V. N., “Jordan superalgebras of vector type and projective modules,” Siberian Math. J., 53, No. 3, 450–460 (2012).zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Shestakov I. P., “Superalgebras and counterexamples,” Siberian Math. J., 32, No. 6, 1052–1060 (1991).MathSciNetCrossRefGoogle Scholar
  13. 13.
    McCrimmon K., “Speciality and non-speciality of two Jordan superalgebras,” J. Algebra, 149, No. 2, 326–351 (1992).zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Swan R. G., “Vector bundles and projective modules,” Trans. Amer. Math. Soc., 105, 264–277 (1962).zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Martinez C. and Zelmanov E., “Specializations of Jordan superalgebras. Dedicated to Robert V. Moody,” Canad. Math. Bull., 45, No. 4, 653–671 (2002).zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

Personalised recommendations