Avoid common mistakes on your manuscript.
In [1] the authors studied irreducible highest weight representations of the simple n-Lie algebra. However, as was pointed out to us by X. Garcia-Martinez, R. Turdibaev, T. van der Linden in [2], Proposition 1 and the results of Section 2 do not hold unless we impose the extra assumption the the n-Lie algebra V is such that
is skew-symmetric. For the simple n-Lie algebra this condition is automatically satisfied, hence the main results of the paper are correct.
We thank X. Garcia-Martinez, R. Turdibaev, T. van der Linden for pointing out this mistake to us.
References
D. Bălibanu, J. van de Leur, Irreducible highest weight representations of the simple n-Lie algebra, Transform. Groups 17 (2012), no. 3, 593-613.
X. Garcia-Martinez, R. Turdibaev, T. van der Linden, Do n-Lie algebras have universal enveloping algebras, arXiv:1508.06940 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
The online version of the original article can be found under doi:10.1007/s00031-012-9189-2.
Rights and permissions
About this article
Cite this article
BĂLIBANU, D., VAN DE LEUR, J. Erratum to: “IRREDUCIBLE HIGHEST WEIGHT REPRESENTATIONS OF THE SIMPLE n-LIE ALGEBRA”, TRANSFORMATION GROUPS 17 (2012), 593–613. Transformation Groups 21, 297 (2016). https://doi.org/10.1007/s00031-015-9359-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00031-015-9359-0