Skip to main content
SpringerLink
Log in

Ideal points of semisimple Jordan algebras

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

It is well known that I. L. Kantor has presented a local construction which assigns to a semisimple Jordan algebra a compact symmetric space with an extendible group of motions. For semisimple Jordan algebras of classical type we present a method of completion of the algebra space to a symmetric space in the large that generalizes the completion of a Euclidean space to a projective space and a conformai sphere.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. I. L. Kantor, “Transitive-differential transformation groups,” Proceed. Seminar on Vector and Tensor Analysis,13, 301–398 (1966).

    Google Scholar 

  2. I. L. Kantor, “General norm of Jordan algebra and the geometry of certain transformation groups,” Proceed. Seminar on Vector and Tensor Analysis,14, 114–143 (1968).

    Google Scholar 

  3. I. L. Kantor, A. I. Sirota, and A. S. Solodovnikov, “A class of Riemann spaces with, an extendible group of motions and a generalization of Poincaré's model,” Dokl. Akad. Nauk SSSR, 173, No. 3, 511–515 (1967).

    Google Scholar 

  4. J. Tits, “Algebres alternatives, algébres de Jordan et groupes de Lie exceptionnels,” Proc. Koningl. Akad. Wetensch.,69, No. 2, 223–237 (1966).

    Google Scholar 

  5. M. Koecher, “Über eine Gruppe rationaler Abbildungen,” Invent. Math.,3, no. 2, 137–218 (1967).

    Google Scholar 

  6. M. Koecher, “Imbedding of Jordan algebras into Lie algebras,” Amer. J. Math.,90, No. 2, 476–510 (1968).

    Google Scholar 

  7. S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York (1962).

    Google Scholar 

  8. H. Braun and M. Koecher, Jordan Algebren, Berlin-Heidelberg-New York (1966).

  9. T. Nagano, “Transformation groups on compact symmetric spaces,” Trans. Amer. Math. Soc.,118, No. 6, 428–453 (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    B. O. Makarevich

Authors
  1. B. O. Makarevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskte Zametki, Vol. 15, No. 2, pp. 295–305, February, 1974.

The author expresses his gratitude to É. B. Vinberg for his aid and steady interests and also to I. L. Kanter for valuable suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makarevich, B.O. Ideal points of semisimple Jordan algebras. Mathematical Notes of the Academy of Sciences of the USSR 15, 168–173 (1974). https://doi.org/10.1007/BF02102401

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02102401

Keywords

Search

Navigation