Skip to main content
SpringerLink
Log in

On definability of addition in Lie algebras

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

An answer is obtained to I. V. Arzhantsev’s question on definability of the structure of a semisimple Lie algebra by the multiplicative groupoid of L.

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. Arzhantsev I. V., “Uniqueness of addition in semisimple Lie algebras,” Russian Math. Surveys, 56, No. 3, 569–571 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  2. Arzhantsev I. V., “Some results on uniqueness of addition in Lie algebras,” in: Proceedings of the 1st Colloquium on Lie Theory and Applications, (Vigo, Spain, July 17–22, 2000), Univ. Vigo, Colecc. Congr., 35, Vigo, 2002, pp. 19–24.

  3. Jacobson N., Lie Algebras, Wiley and Sons, New York etc. (1962).

    MATH  Google Scholar 

  4. Ponomarev K. N., “Automorphisms group of an invariant subalgebra of a reductive Lie algebra,” Acta Appl. Math., 85, No. 1–3, 251–255 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  5. Ponomarev K. N., Rigid Algebras and Nonassociative Rings [in Russian], Izdat. NGTU, Novosibirsk (2007).

    Google Scholar 

  6. Vinberg È. B., Gorbatsevich V. V., and Onishchik A. L., “The structure of Lie groups and Lie algebras,” in: Contemporary Problems of Mathematics. Fundamental Trends. Vol. 41 [in Russian], VINITI, Moscow, 1990, pp. 5–258. (Itogi Nauki i Tekhniki.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    K. N. Ponomarev

Authors
  1. K. N. Ponomarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. N. Ponomarev.

Additional information

Original Russian Text Copyright © 2011 Ponomarev K. N.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 6, pp. 1341–1345, November–December, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ponomarev, K.N. On definability of addition in Lie algebras. Sib Math J 52, 1065–1068 (2011). https://doi.org/10.1134/S0037446611060115

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446611060115

Keywords

Search

Navigation