Skip to main content
SpringerLink
Log in

Identities of representations of Lie algebras and *-polynomial identities

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In this paper we have found a necessary and sufficient condition for the existence of *-identities of special kind and in skew-symmetric variables in matrix algebras with symplectic involution *. The same result holds for the identities of the natural representation of the symplectic simple Lie algebra.

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

References

  1. G. M. Bergman,Wild automorphisms of free P.I. algebras and some new identities, preprint.

  2. N. Bourbaki,Groupes et Algèbres de Lie, Chs. VII, VIII Hermann, Paris, 1975.

    MATH  Google Scholar 

  3. M. Domokos,Gröbner bases, determinantal ideals and identities of matrices, in preparation.

  4. V. Drensky, Ts. Rashkova,Weak polynomial identities for the matrix algebra, Commun. in Algebra21 (1993), 3779–3795.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. Formanek,Central polynomials for matrix rings, J. Algebra23 (1972), 129–132.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Giambruno, A. Valenti,On minimal *-identities of matrices, Linear Multilin. Algebra39 (1995), 309–323.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Halpin,Central and weak identities for matrices, Commun. in Algebra11 (1983), 2237–2248.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yu. P. Razmyslov,On a problem of Kaplansky (Russian), Izv. Akad. Nauk SSSR, Ser. Mat.37 (1973), 483–501. Translation: Math. USSR Izv.7 (1973), 479–496.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre of Mathematics, University of Rousse “A. Kanchev”, Studentska Str. 8, 7017, Rousse, Bulgaria

    Tsetska Rashkova

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., block 8, 1113, Sofia, Bulgaria

    Vesselin Drensky

Authors
  1. Tsetska Rashkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vesselin Drensky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tsetska Rashkova.

Additional information

Partially supported by Grant MM605/96 of the Bulgarian Foundation for Scientific Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rashkova, T., Drensky, V. Identities of representations of Lie algebras and *-polynomial identities. Rend. Circ. Mat. Palermo 48, 153–162 (1999). https://doi.org/10.1007/BF02844386

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02844386

Keywords

Search

Navigation