Skip to main content
SpringerLink
Log in

RESTRICTED CARTAN TYPE LIE ALGEBRAS AND THE COADJOINT REPRESENTATION

  • Published:
Transformation Groups Aims and scope Submit manuscript

Abstract

Let L be a restricted Cartan type Lie algebra over an algebraically closed field k of characteristic p > 3, and let G denote the automorphism group of L. We prove that there are no nontrivial invariants of L ∗ under the coadjoint action, i.e., k[L ∗]G = k. This property characterises the Cartan type algebras among the restricted simple Lie algebras.

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. Benkart, T. Gregory, A. Premet, The Recognition Theorem for Graded Lie Algebras in Prime Characteristic, Mem. Amer. Math. Soc. 197 (920) (2009), no. 920, xii+145 pp.

  2. J.-M. Bois, R. Farnsteiner, B. Shu, Weyl groups for non-classical restricted Lie algebras and the Chevalley Restriction Theorem, Forum Math. 26 (2014), no. 5, 1333–1379.

  3. R. Farnsteiner, H. Strade, Modular Lie Algebras and Their Representations, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 116, Marcel Dekker, New York, 1988.

  4. R. R. Holmes, C. Zhang, Some simple modules for the restricted Cartan-type Lie algebras, J. Pure Appl. Algebra 173 (2002), no. 2, 135–165.

  5. M. Mygind, Orbit closures in the Witt algebra and its dual space, J. Algebra and its Appl. 13 (2014), no. 5, doi:10.1142/S0219498813501466.

  6. A. Премет, Теорема об ограничении инварианmов и нильnоmенmные злeмeнmы в W n , Мат. сб. 182 (1991), no. 5, 746–773. Engl. transl.: A. Premet, The theorem on restriction of invariants and nilpotent elements in W n , Mathematics of the USSR-Sbornik 73 (1992), no. 1, 135–159.

  7. A. Premet, H. Strade, Simple Lie algebras of small characteristic VI. Completion of the classification, J. Algebra 320 (2008), no. 9, 3559–3604.

  8. R. L. Wilson, Automorphisms of graded Lie algebras of Cartan type, Comm. Algebra 3 (1975), no. 7, 591–613.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Aarhus University, 8000, Aarhus, Denmark

    MARTIN MYGIND

Authors
  1. MARTIN MYGIND
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to MARTIN MYGIND.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

MYGIND, M. RESTRICTED CARTAN TYPE LIE ALGEBRAS AND THE COADJOINT REPRESENTATION. Transformation Groups 20, 495–505 (2015). https://doi.org/10.1007/s00031-014-9295-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00031-014-9295-4

Keywords

Search

Navigation