Skip to main content
Log in

Lie-Kac bigroups

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We define the Lie-Kac bigroups as special double Hilbert algebras canonically associated with ring groups (the Kac algebras) and related to the Lie bialgebras.

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

Access this article

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

References

  1. V. G. Drinfel’d “Hamiltonian structures on Lie groups, Lie bialgebras, and the geometric meaning of the classical Yang-Baxter equations,” Dokl. Akad. Nauk SSSR, 268, No. 2, 285–287 (1983).

    MathSciNet  Google Scholar 

  2. G. I. Kac, “Ring groups and duality principle,” Tr. Most Mat. Obshch., 12, 259–301 (1963).

    Google Scholar 

  3. G. I. Kac, “Ring groups and duality principle. II,” Tr. Mosk. Mat. Obshch., 13, 83–113 (1965).

    Google Scholar 

  4. P. J. Dixmier, Les C*-Algèbres et Leurs Représentations, Gauthier-Villars, Paris 1969.

    Google Scholar 

  5. G. I. Kac and V. G. Palyutkin, “An example of a ring group generated by Lie groups.” Ukr. Mat. Zh., 16, No. 1, 99–105 (1964).

    Google Scholar 

  6. M. Enock and L. Vainerman, “Deformation of Kac algebras by Abelian subgroups,” Commun. Math. Phys., 178, 571–596 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  7. G. I. Kac, “Extensions of groups that are ring groups,” Mat. Sb., 76, Issue 3, 473–196 (1968).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palyutkin, V.G. Lie-Kac bigroups. Ukr Math J 52, 754–764 (2000). https://doi.org/10.1007/BF02487287

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487287

Keywords

Navigation