Skip to main content
SpringerLink
Log in

Jordan–Kronecker invariants for semidirect sums defined by standard representation of orthogonal or symplectic Lie algebras

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

We calculate Jordan–Kronecker invariants for semi-direct sums of Lie algebras so(n) and sp(n) with several copies of Rn with respect to their standard representation.

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. A. V. Bolsinov and P. Zhang, “Jordan–Kronecker invariants of finite-dimensional Lie algebras,” Transform. Groups 21, 51–86 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  2. A. V. Bolsinov, “Liouville integrable Hamiltonian systems on Lie algebras,” Cand. Sci.Dissertation (Moscow State Univ.,Moscow, 1987).

    Google Scholar 

  3. A. V. Bolsinov, A. M. Izosimov, A. Yu. Konjaev, and A. A. Oshemkov, “Algebra and topology of integrable systems. Research problems,” Tr. Sem. Vektor. Tenzor. Anal. 28, 119–191 (2012).

    Google Scholar 

  4. A. Bolsinov, A. Izosimov, and D. Tsonev, “Finite-dimensional integrable systems: A collection of research problems,” J. Geom. Phys. (2016). doi 10.1016/j.geomphys.2016.11.003

    Google Scholar 

  5. A. Gusejnov, “Coadjoint invariants of Lie algebras so(n) +φ (R n)k, sp(n) +φ (R n)k, gl(n)+φ (R n)k,” Graduation Paper (Moscow State Univ.,Moscow, 2006).

    Google Scholar 

  6. A. S. Mischenko and A. T. Fomenko, “Euler equations on finite-dimensional Lie groups,” Math. USSR Izv. 12, 371–389 (1978).

    MATH  Google Scholar 

  7. M. Rais, “L’indice des produits semidirects \(E\mathop \times \limits_\rho G\) ,” C. R. Acad. Sci. Paris, Ser. A 287, 195–197 (1978).

    Google Scholar 

  8. S. Rosemann and K. Schöbel, “Open problems in the theory of finite-dimensional integrable systems and related fields,” J. Geom. Phys. 87, 396–414 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Thompson, “Pencils of complex and real symmetric and skew matrices,” Linear Algebra Appl. 147, 323–371 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Vorontsov, “Kronecker indices of Lie algebras and invariants degrees estimate,” Moscow Univ.Math. Bull. 66, 26–30 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Vorontsov, “Invariants of Lie algebras representable as semidirect sums with a commutative ideal,” Sb. Math. 200 (8), 45–62 (2009).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    K. Vorushilov

Authors
  1. K. Vorushilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Vorushilov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vorushilov, K. Jordan–Kronecker invariants for semidirect sums defined by standard representation of orthogonal or symplectic Lie algebras. Lobachevskii J Math 38, 1121–1130 (2017). https://doi.org/10.1134/S1995080217060142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080217060142

Keywords and phrases

Search

Navigation