Skip to main content
Log in

Simple Lie sheaves of small dimension

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We classify simple Lie sheaves of dimension at most 4.

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.

Similar content being viewed by others

References

  1. Kantor I. L. and Persits D. B., “On closed sheaves of linear Poisson brackets,” in: IX All-Union Geometric Conference, Shtiintsa, Kishinëv, 1988, p. 141.

    Google Scholar 

  2. Olver P. J., Applications of Lie Groups to Differential Equations, Springer-Verlag, New York (1993).

    Book  MATH  Google Scholar 

  3. Trofimov V. V. and Fomenko A. T., Algebra and Geometry of Integrable Hamiltonian Differential Equations [in Russian], Factorial, Prosperius, and Udmirt. State Univ., Izhevsk (1995).

    Google Scholar 

  4. Koreshkov N. A., “Nilpotency of n-tuple Lie algebras and associative n-tuple algebras,” Russian Math. (Iz. VUZ), 54, No. 2, 28–32 (2010).

    MATH  MathSciNet  Google Scholar 

  5. Koreshkov N. A., “Lie and Engel theorems for n-tuple Lie algebras,” Siberian Math. J., 54, No. 3, 472–478 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  6. Dotsenko V. V. and Khoroshkin A. S., “Character formulas for the operad of two compatible brackets and for the bi-Hamiltonian operad,” Funct. Anal. Appl., 41, No. 1, 1–17 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  7. Filippov V. T., “n-Lie algebras,” Siberian Math. J., 26, No. 6, 879–891 (1985).

    Article  MATH  Google Scholar 

  8. Koreshkov N. A., “Lie sheaves of small dimensions,” Russian Math. (Iz. VUZ), 57, No. 11, 1–16 (2013).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. A. Koreshkov.

Additional information

Original Russian Text Copyright © 2014 Koreshkov N.A.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 525–539, May–June, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koreshkov, N.A. Simple Lie sheaves of small dimension. Sib Math J 55, 428–439 (2014). https://doi.org/10.1134/S0037446614030045

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446614030045

Keywords

Navigation