Skip to main content
Log in

n-Lie Structures That Are Generated by Wronskians

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We study the (k + 1)-Lie structures, k-left commutative and homotopy (k + 1)-Lie structures with multiplication generated by Wronskians and prove that the nontrivial structures of n-Lie algebras appear only in the case of small characteristic.

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. Filippov V. T., “n-Lie algebras,” Sibirsk. Mat. Zh., 26, No.6, 126–140 (1985).

    Google Scholar 

  2. Filippov V. T., “On the n-Lie algebra of Jacobians,” Sibirsk. Mat. Zh., 39, No.3, 660–669 (1998).

    Google Scholar 

  3. Kurosh A. G., “Multioperator rings and algebras,” Uspekhi Mat. Nauk, 24, No.1, 3–15 (1969).

    Google Scholar 

  4. Stasheff J. and Lada T., “Introduction to SH Lie algebras for physicists,” Internat. J. Theoret. Phys., 32, No.7, 1087–1103 (1993).

    Article  Google Scholar 

  5. Hanlon P. and Wachs M., “On Lie k-algebras,” Adv. Math., 113, 206–236 (1995).

    Article  Google Scholar 

  6. Loos O., Symmetric Spaces [Russian translation], Nauka, Moscow (1985).

    Google Scholar 

  7. Skryabin S. M., “New series of simple Lie algebras of characteristic 3,” Mat. Sb., 183, No.8, 3–22 (1992).

    Google Scholar 

  8. Pozhidaev A. P., “Two classes of central simple n-Lie algebras,” Sibirsk. Mat. Zh., 40, No.6, 1313–1322 (1999).

    Google Scholar 

  9. Dzhumadil’daev A. S., “A remark on the space of invariant differential operators,” Vestnik Moskov. Univ. Ser. I Mat. Mekh., 116, No.2, 49–54 (1982).

    Google Scholar 

  10. Dzhumadil’daev A. S., “On the integral and mod p-cohomologies of the Lie algebra W 1,” Funktsional. Anal. i Prilozhen., 22, No.3, 68–70 (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text Copyright © 2005 Dzhumadil’daev A. S.

__________

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 759–773, July–August, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dzhumadil’daev, A.S. n-Lie Structures That Are Generated by Wronskians. Sib Math J 46, 601–612 (2005). https://doi.org/10.1007/s11202-005-0061-7

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-005-0061-7

Keywords

Navigation